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**The Mathematics of Chemistry**

4 5 Significant Figures 2 8

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**Uncertainty of Measurement**

The last digit on any physical measurement is always an approximation. Significant figures are the number of digits that can be accurately measured and the first uncertain digit.

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**Rules for Finding Significant Figures**

All nonzero digits are significant.

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**Rules for Finding Significant Figures**

All sandwiched zeros are significant.

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**Rules for Finding Significant Figures**

All zeros to the right of all non-zero digits are only significant if a decimal point is shown.

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**Rules for Finding Significant Figures**

All leading zeros before the first nonzero digit are NOT significant.

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**Total Significant Figures?**

9

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**How many significant figures?**

800.1 4

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**How many significant figures?**

5

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**How many significant figures?**

800 1

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**How many significant figures?**

800.* 3 *Trailing zeros to the right of a non-zero digit are not significant unless they are followed by a decimal point.

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**How many significant figures?**

0.008 1

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**How many significant figures?**

0.180 3

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**Using significant figures when adding and subtracting.**

When adding or subtracting amounts of substance, the final amount can only be as precise as the least precise number in the calculation. If you add 0.03 g of NaCl to 155 g of water, the total mass should be expressed as 155 g because the mass of water has the least precise measurement.

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**Using significant figures when adding and subtracting.**

Find the number of significant figures in the decimal portion of each of the numbers in the problem. Add or subtract the numbers. Round the answer to match the least number of places in the decimal portion of any number in the problem.

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**Using significant figures when adding and subtracting.**

20.629 0.18 4.20 3 3 2 + 2 The least amount of significant figures to the right of the decimal in the numbers is 2. Therefore the answer should only have 2 significant figures to the right of the decimal. 917.55

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**Using significant figures when multiplying and dividing.**

When multiplying or dividing numbers the answer should have the same number of significant figures as the least precise number.

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**Using significant figures when multiplying and dividing.**

Find the number of significant figures in each of the numbers involved in the calculation. Complete the calculation. Write the answer in the number of significant figures as the beginning number with the least significant figures.

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**Using significant figures when multiplying and dividing.**

28.3 X 5.0 = 141.5 28.3 has 3 significant figures and 5.0 has 2 significant figures, therefore the answer should be written 140 so that it only has 2 significant figures. 140

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