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**Measurement & Significant Figures**

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What time is it? Someone might say: “9:00” or “9:02” or “9:02:22” All of these are appropriate for different situations But why is it we can read so many different times from a clock?

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**Each time given depends on…**

what type of clock a person is reading! The clock here shows the hours and 5 minute increments. What time is it on this clock? 10:10:00 10:10

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**Can we really read seconds from this clock?**

This clock has no second hand, so we don’t know if it is 10:10:00 or 10:10:30. This clock has a limit to what time it can tell.

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You’re RIGHT!!! This clock has no second hand, so we don’t know if it is 10:10:00 or 10:10:30. This clock has a limit to what time it can tell.

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**Each time given depends on…**

what type of clock a person is reading! The clock here shows the hours and each minute increment. If the minute hand was here, What time is it? 10:10 10:12 10:12:00

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Not Exactly… This clock has minute increments. So the time can be read more accurately. TRY AGAIN!

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GREAT!!!! This clock has minute increments so you can tell it is exactly on the 12. But it still doesn’t have a second hand, so we can’t include seconds in our time.

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Not Exactly… The clock here shows the hours and each minute increment. But the clock still does not display time in seconds. TRY AGAIN!

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**Each time given depends on…**

what type of clock a person is reading! The clock here shows the hours, minutes, and seconds. If the minute hand was here What time is it? 10:10 10:12 10:12:32

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Not Exactly… This clock has minute increments and a sec hand. So the time can be read more accurately. TRY AGAIN!

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Not Exactly… This clock has minute increments and a sec hand. So the time can be read more accurately. TRY AGAIN!

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Fantastic!!!! This clock has minute increments and a second hand. The time can be read more accurately on this clock!

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**we are taking a measurement!**

When we read time… we are taking a measurement! How exact our measurement is depends on the equipment or instrument we use to take that measurement.

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**Let’s look at another example:**

The person reading this green object records the length as Based on the instrument they are using, is this a valid measurement? Yes No

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Excellent!!! This ruler does not have enough increments to measure the object to 5 decimal places. A measurement of 4.8 would be more accurate.

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Take Another Look… How many increments are listed on the ruler? Can you see enough increments to read out 5 decimal places? No! Therefore, a measurement of 4.8 would be more accurate.

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**Now you try… What is the length of this gray block in cm? 11.6 11.71**

How long is the grey block above? 11.6 11.71 11.65 11.7

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Let’s look Closer … Looking at the red line, you can see that there is still some of the grey block that passes the line. Therefore, is too small of a measurement for this block. TRY AGAIN! This is the line for .6

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Let’s look Closer … Looking at the red line, you can see that the grey block does not reach the line. Therefore, the measurement 11.7 is too big for this block. TRY AGAIN! This is the line for .7

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Great Job!!! Looking at the red line, you can see the line lies right between .6 and .7! Therefore, the correct measurement needs to include the .6 but also an extra digit to indicate the block passes the .6 but does not reach .7… so does just that! This is the line for .6

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Let’s look Closer … Looking at the red line, you can see that the grey block does not reach the line. Therefore, the measurement is too big for this block. TRY AGAIN! This is the line for .7

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**Graduated Cylinders Are used to measure the volume of a liquid**

Always, record the measurements from the bottom of the meniscus.

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**The meniscus occurs from liquid being in the graduated cylinder.**

To ensure an accurate measurement, you should always read from the bottom of the meniscus.

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**Look at the graduated cylinder at the right.**

What would be the volume of the liquid? 54 53 54.1 52.9

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**The yellow line indicates the increment for 54**

The yellow line indicates the increment for 54. Is the bottom of the meniscus at this line? No it isn’t. TRY AGAIN!

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**The yellow line indicates the increment for 53**

The yellow line indicates the increment for 53. Is the bottom of the meniscus at this line? Almost, but you can still see a bit of the liquid line. TRY AGAIN!

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**The yellow line indicates the increment for 51. 2**

The yellow line indicates the increment for Is the bottom of the meniscus at this line? No it isn’t. TRY AGAIN!

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**The yellow line indicates the increment for 52**

The yellow line indicates the increment for You can no longer see the meniscus. But the liquid level is not quite at 53 because you can see the 53 increment right above the yellow line.

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**Measurements in Science**

In science, we describe a measurement as having a certain number of “significant digits” These are called significant digits, significant figures, or sometimes just “Sig Figs”.

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**Significant Figures or “Sig Figs”**

Remember: significant figures, significant digits, and sig figs mean the same

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This clock reads “9:02:22” In this measurement, all the numbers are important to the specific time. Therefore, this time has 5 significant digits or figures.

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**Remember… This block has a measurement of 11.65.**

Each digit in the measurement is significant. Therefore, this measurement has 4 significant figures or “sig figs” This is the line for .6

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When reading the bottom of this meniscus, the liquid is right at the 32 increment. However, to indicate this, the measurement needs a .0 added. There are 3 sig figs in this measurement

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**Let’s take a look at the rules!!!**

Determining Sig Figs There are rules that dictate the number of significant digits in a measurement. Let’s take a look at the rules!!!

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**Sig Fig Rules: Significant**

Non-Zeros: 1) All non-zeros are significant (1-9) Examples: = Sig Figs = Sig Figs

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**Sig Fig Rules: Significant**

Zeros 2) Zeros appearing between non-zero digits are significant Examples: = 7 Sig Figs = Sig Figs

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**Sig Fig Rules: Significant**

Zeros: 3) Zeros at the end of a number and to the right of a decimal point are significant Examples: = 6 Sig Figs = Sig Figs

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**Sig Fig Rules: Significant**

Zeros: 4) Zeros at the end of a number and to the left of a decimal point are significant Examples: = 6 Sig Figs = Sig Figs

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**Sig Fig Rules: Non-Significant**

Zeros: 5) Place keeping zeros are not significant A) In front of non-zero digits B) End of a number without a decimal Examples: = 4 Sig Figs Not Significant = Sig Figs

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**How many sig figs does the following number have? 246783972**

Now Let’s Practice!!! How many sig figs does the following number have? 8 9

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**Remember your Rules: TRY AGAIN 246783972**

All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal TRY AGAIN

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**Great!!! Now which Rule did you use?**

1. All non-zeros are significant (1-9) 2. Zeros appearing between non-zero digits are significant 3. Zeros at the end of a number and to the right of a decimal point are significant 4. Zeros at the end of a number and to the left of a decimal point are significant 5. Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal

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Remember your Rules: All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal Are there zeros in your value? Where are they located? If the zeros are not between to non-zero digits, you used a different rule. TRY AGAIN

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Remember your Rules: All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal Are there zeros in your value? Where are they located? Is there a decimal present? If there is no decimal or if the zeros are not to the right of the decimal, then you used a different rule. TRY AGAIN

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Remember your Rules: All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal Are there zeros in your value? Where are they located? Is there a decimal present? If there is no decimal or the zeros are not to the left of the decimal, you used a different rule. TRY AGAIN

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Remember your Rules: All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal Are there zeros in your value? Where are they located? Is there a decimal present? If the zeros are in front of any non-zero digit, or if the zeros are at the end of a number without a decimal, you used a different rule. TRY AGAIN

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**Great!!! Let’s Try Another One…**

How many sig figs does the following number have? 7 3 8

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**Remember your Rules: TRY AGAIN 0.0000784**

All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal TRY AGAIN

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**Awesome!!! Now which Rule did you use?**

1. All non-zeros are significant (1-9) 2. Zeros appearing between non-zero digits are significant 3. Zeros at the end of a number and to the right of a decimal point are significant 4. Zeros at the end of a number and to the left of a decimal point are significant 5. Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal

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**Remember your Rules: 0.0000784 Are all the digits between 1-9?**

All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal Are all the digits between 1-9? If there is one zero, you used a different rule. TRY AGAIN

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Remember your Rules: All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal Are there zeros in your value? Where are they located? If the zeros are not between to non-zero digits, you used a different rule. TRY AGAIN

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Remember your Rules: All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal Are there zeros in your value? Where are they located? Is there a decimal present? If there is no decimal or if the zeros are not at the end of a number and to the right of the decimal, then you used a different rule. TRY AGAIN

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Remember your Rules: All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal Are there zeros in your value? Where are they located? Is there a decimal present? If there is no decimal or the zeros are not to the left of the decimal, you used a different rule. TRY AGAIN

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**You really know your stuff! Let’s Try Another…**

How many sig figs does the following number have? 2 4 7

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**Remember your Rules: TRY AGAIN 6300045**

All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal TRY AGAIN

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**Fantastic!!! Now which Rule did you use?**

1. All non-zeros are significant (1-9) 2. Zeros appearing between non-zero digits are significant 3. Zeros at the end of a number and to the right of a decimal point are significant 4. Zeros at the end of a number and to the left of a decimal point are significant 5. Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal

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**Remember your Rules: 6300045 Are all the digits between 1-9?**

All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal Are all the digits between 1-9? If there is one zero, you used a different rule. TRY AGAIN

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Remember your Rules: All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal Are there zeros in your value? Where are they located? Is there a decimal present? If there is no decimal or if the zeros are not to the right of the decimal, then you used a different rule. TRY AGAIN

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Remember your Rules: All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal Are there zeros in your value? Where are they located? Is there a decimal present? If there is no decimal or the zeros are not to the left of the decimal, you used a different rule. TRY AGAIN

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Remember your Rules: All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal Are there zeros in your value? Where are they located? Is there a decimal present? If the zeros are in front of any non-zero digit, or if the zeros are at the end of a number without a decimal, you used a different rule. TRY AGAIN

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**Yes!!! You got it!! Do Another…**

How many sig figs does the following number have? 34 17 2

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**Remember your Rules: TRY AGAIN All non-zeros are significant (1-9)**

Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal TRY AGAIN

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**Great Job!!! Now which Rule did you use?**

1. All non-zeros are significant (1-9) 2. Zeros appearing between non-zero digits are significant 3. Zeros at the end of a number and to the right of a decimal point are significant 4. Zeros at the end of a number and to the left of a decimal point are significant 5. Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal

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**Remember your Rules: Are all the digits between 1-9?**

All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal Are all the digits between 1-9? If there is one zero, you used a different rule. TRY AGAIN

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Remember your Rules: All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal Are there zeros in your value? Where are they located? If the zeros are not between to non-zero digits, you used a different rule. TRY AGAIN

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Remember your Rules: All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal Are there zeros in your value? Where are they located? Is there a decimal present? If there is no decimal or if the zeros are not to the right of the decimal, then you used a different rule. TRY AGAIN

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Remember your Rules: All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal Are there zeros in your value? Where are they located? Is there a decimal present? If there is no decimal or the zeros are not to the left of the decimal, you used a different rule. TRY AGAIN

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**Great Work!! Here’s Another…**

How many sig figs does the following number have? 2 13 8

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**Remember your Rules: TRY AGAIN 1300000000000.**

All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal TRY AGAIN

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**Nice Work!!! Now which Rule did you use?**

1. All non-zeros are significant (1-9) 2. Zeros appearing between non-zero digits are significant 3. Zeros at the end of a number and to the right of a decimal point are significant 4. Zeros at the end of a number and to the left of a decimal point are significant 5. Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal

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**Remember your Rules: 1300000000000. Are all the digits between 1-9?**

All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal Are all the digits between 1-9? If there is one zero, you used a different rule. TRY AGAIN

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Remember your Rules: All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal Are there zeros in your value? Where are they located? If the zeros are not between to non-zero digits, you used a different rule. TRY AGAIN

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Remember your Rules: All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal Are there zeros in your value? Where are they located? Is there a decimal present? If there is no decimal or if the zeros are not to the right of the decimal, then you used a different rule. TRY AGAIN

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Remember your Rules: All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal Are there zeros in your value? Where are they located? Is there a decimal present? If the zeros are in front of any non-zero digit, or if the zeros are at the end of a number without a decimal, you used a different rule. TRY AGAIN

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**How many sig figs does the following number have? 3.400**

Hooray!!! Just one More… How many sig figs does the following number have? 3.400 4 2

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**Remember your Rules: TRY AGAIN 3.400**

All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal 3.400 TRY AGAIN

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**Great!!! Now which Rule did you use?**

1. All non-zeros are significant (1-9) 2. Zeros appearing between non-zero digits are significant 3. Zeros at the end of a number and to the right of a decimal point are significant 4. Zeros at the end of a number and to the left of a decimal point are significant 5. Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal

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**Remember your Rules: 3.400 Are all the digits between 1-9?**

All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal 3.400 Are all the digits between 1-9? If there is one zero, you used a different rule. TRY AGAIN

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Remember your Rules: All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal 3.400 Are there zeros in your value? Where are they located? If the zeros are not between to non-zero digits, you used a different rule. TRY AGAIN

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Remember your Rules: All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal 3.400 Are there zeros in your value? Where are they located? Is there a decimal present? If there is no decimal or the zeros are not to the left of the decimal, you used a different rule. TRY AGAIN

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Remember your Rules: All non-zeros are significant (1-9) Zeros appearing between non-zero digits are significant Zeros at the end of a number and to the right of a decimal point are significant Zeros at the end of a number and to the left of a decimal point are significant Place keeping zeros are NOT significant: In front of non-zero digits End of a number without a decimal 3.400 Are there zeros in your value? Where are they located? Is there a decimal present? If the zeros are in front of any non-zero digit, or if the zeros are at the end of a number without a decimal, you used a different rule. TRY AGAIN

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YAY!!! You Did It!!! Great Work!!!! When taking measurements or using measurements in science, Remember to use significant figures. Significant figures or digits will be important to many of the concepts and topics you will learn in chemistry this year.

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