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**Scientific Measurement**

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**Are you ready for today? Yes No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16**

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**Accuracy - How close a measurement is to the true value**

Precision - How close a set of measurements are to one another.

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**How accurate or precise was this person?**

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**Precise or Accurate? Accurate Precise Both Neither 1 2 3 4 5 6 7 8 9**

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**Precise or Accurate? Accurate Precise Both Neither 1 2 3 4 5 6 7 8 9**

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Scientific Notation all numbers are expressed as whole numbers between 1 and 9 multiplied by a whole number power of 10. Ex = 1.25 x 102 = x 10-5

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You try some... Write the following numbers in scientific notation: A) 5,000 E) B) 34,000 F) C) 1,230,000 G) D) 5,050,000,000 H)

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**Significant Figures or Digits**

Significant Figures are used to show the accuracy and precision of the instruments used to take the measurement.

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**What is the measurement?**

1 .5 1 1

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**What is the measurement?**

1 0.55 0.7 0.6 0.8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

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**What is the measurement?**

1 0.55 0.70 0.67 0.65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

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**Measurements To show how precise the instrument is:**

Read the measurement to one decimal place what the instrument is marked

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Read the water level 4.85 7.2 4.3 4.35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

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Read the water level 17.0 16.8 15.18 15.2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

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**Counting Significant Digits**

Non-zero digits are always significant 1,2,3,4,5,6,7,8,9 are always significant Rules for Zeros: Leading Zeros never count as significant Captive zeros (zeros between non-zero digits) are always significant 10, Trailing Zeros are significant ONLY IF there is a decimal in the number. 234, ,

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If we want to write the number 700 with 3 significant digits we can do so using the following two methods: OR ×102

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You try some... How many significant digits do the following numbers have? A) 20 F) 7.00 K) 65,060 B) 22.0 G) 87,001 L) C) 20.1 H) M) D) 56,000 I) N) 4.30×104 E) 75,000. J) 570 O)

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**How many significant digits does the following number have? 20**

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**How many significant digits does the following number have? 22.0**

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**How many significant digits does the following number have? 0.000354**

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**How many significant digits does the following number have? 56,000**

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**How many significant digits does the following number have? 75,000.**

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**How many significant digits does the following number have? 7.00**

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**How many significant digits does the following number have? 4.30 x 108**

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**How many significant digits does the following number have? 0.00040050**

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**How many significant digits does the following number have? 0.00043**

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**How many significant digits does the following number have? 10,023,000**

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Pair-up Exercise You and a partner will practice your significant digits. Your job is to come up with a number containing both zeroes and non-zero digits. You will trade boards back and forth – on my mark. The partner that gets the correct number of significant digits will get the point. The partner with the most points will win the round. We will do best of 9.

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**Rounding Numbers to the Correct Significant Figures**

Count (from left to right) how many significant figures you need. Look at the next number to see if you need to round your last sig. fig. up or down. Round the following to 3 sig. figs 1,344 24,500 12,345 x 10-3

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**Significant Digit Calculations**

We have two ways of categorizing sig. fig. calculations: Addition and Subtraction B) Multiplication, Division, other math

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**Addition and Subtraction Rules**

When we add and subtract we are only worried about the number of decimal places involved in the numbers present. We do not care about the number of actual significant digits. We will always pick the number that has the least decimal places.

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You try some... A) B) C) D) 100 – 5.8 E) 2.5 – 1.25 F) – 32.11

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**Tens Ones Tenths Hundreths**

To what decimal place/place value should the following answer be rounded to Tens Ones Tenths Hundreths 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

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**Tens Ones Tenths hundreths**

To what decimal place/place value should the following answer be rounded to Tens Ones Tenths hundreths 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

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**Ones Tenths Hundreths Thousandths Ten thousandths**

To what decimal place/place value should the following answer be rounded to Ones Tenths Hundreths Thousandths Ten thousandths 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

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**Hundreds Tens Ones tenths**

To what decimal place/place value should the following answer be rounded to Hundreds Tens Ones tenths 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

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**Multiplication, Division, other math**

If we are multiplying, dividing, using exponents, trigonometry, calculus, etc we must use the least number of significant digits of the numbers in the set. For example...

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You try some... A) 12 × 5.00 F) 119 / 32 B) 8.45 × 4.3 G) / 29.8 C) × H) / D) 5.6 × 11.7 I ) 981 / E) 34.1 × 0.55 J) 43.2 / 12.45

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**How many sig. figs. Should your answer be reported in for the following: 12 × 5.00**

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Density Density – the amount of matter present in a given volume of a substance, the ratio of the mass of an object to its volume. D = mass Volume

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Percent Error

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Temperature Celsius Scale – based on the freezing point (0oC) and boiling point (100oC) of water. Kelvin Scale – based on absolute zero (the temperature at which all motion ceases). 1 degree Kelvin is equal to 1 degree Celsius. Fahrenheit Scale – used in US and Great Britain. Degrees are smaller than a Celsius or Kelvin degree.

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**Conversions between temperature scales**

Kelvin/Celsius K = oC + 273 Fahrenheit/Celsius oF = 1.80(oC)

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**Exact Numbers are counting numbers or defined numbers (such as 2**

Exact Numbers are counting numbers or defined numbers (such as 2.45 cm = 1 in) - never limit the number of significant figures in a calculation.

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