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**Significant Figures, and Scientific Notation**

The valid measurements or digits are called SIGNIFICANT!

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When using our calculators we must determine the correct answer; our calculators are mindless drones and don’t know the correct answer.

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**Significant figures are all the digits in a measurement that are known with certainty**

plus a last digit that must be estimated.

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**Uncertainties of Measurements**

Accuracy is the degree of “exactness” to which the measurement quantity can be reproduced.

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Accuracy Is the extent to which a measured value agrees with the standard value of the quantity. CALCULATORS DO NOT INCREASE THE ACCURACY!

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**Using Significant Figures reflects precision by estimating the last digit**

What is the certain measurement? (52 ml) What is the estimated measurement? (.8 ml)

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**The instrument determines the amount of precision of the data.**

What is the certain measurement here? (62.4 g) What is the estimated measurement here? (.00 g)

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**Error vs. Mistakes ERROR MISTAKES Mistakes are caused by PEOPLE**

Scientific errors are caused by INSTRUMENTS Scientific measurements vary in their level of certainty Mistakes are caused by PEOPLE Misreading, dropping, or other human mistakes are NOT error

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**Significant Digits Nonzero digits are always significant**

All final zeros after the decimal point are significant Zeros between two other significant digits are always significant Zeros used solely for spacing the decimal point are not significant

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**Exact and Counting Numbers do not have significant digits**

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**Exact numbers are important: they are infinitely valuable**

Exact numbers are important: they are infinitely valuable. Counting numbers come only in whole numbers.

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**There are rules for: multiplication/division addition/subtraction and combined equations**

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**The answer can’t be more precise than the question**

Rules for multiplication/division The result has the same number of significant figures as the factor with the fewest significant figures The answer can’t be more precise than the question

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**The answer can’t be more precise than the question**

Rules for addition/subtraction The result has the same number of decimal places as the number with the fewest decimal places The answer can’t be more precise than the question

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**1. Do the functions in parenthesis**

2. Note the number of significant digits in the question 3. Perform the remainder of calculations 4. Round the final answer

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**Calculations Addition/Subtraction Multiplication/Division**

The answer is based on the number with the fewest decimal points Multiplication/Division The answer is based on the number with the fewest significant digits

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**Round only the final answer in a series of calculations**

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**Now You Try It! Add 24.686 m +2.343 m + 3.21 m = ?**

Calculator says: 3 decimals, 3 decimals and 2 decimals So 2 decimals it is Answer is m Multiply 3.22 cm by 2.1 cm Calculator says 3 sig figs, 2 sig figs So 2 it is! Answer is 6.8 cm2

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**Divide .005673 L by 2.1 L Calculator says 0.0027014286**

4 sig figs and 2 sig figs 2 it is! Answer is L

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Scientific Notation In chemistry we often use very large or very small numbers We also have to pay attention to significant figures Scientific notation allows us to do both easily!

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**Scientific Notation is using powers of ten**

1000 becomes 1 X 10 3 becomes 1 X

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Try These 3.45 x 104 2.36 x 10-3 5.69 x 107 x 10-7

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**How to do problems with scientific notation Ex. 4. 7 x 10 25 x 1**

How to do problems with scientific notation Ex. 4.7 x x 1.9 x first do numbers: 4.7 x 1.9 estimate as 5 x 2 = 10 now do powers: x = 12 so 10 x or 1.0 x 10 13

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**Calculators can help First, type in the number (ie 4.5) Then press 2nd**

Finally, press EE (above the comma) The number will display as 4.5 E 13 Read this as 4.5 x 10 13

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**Significant figures are easy when using scientific notation 2**

Significant figures are easy when using scientific notation 2.3 x has 2 sig figs 3.7 x has 2 sig figs The placeholder zeros are eliminated for you!

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