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Significant Figures

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**Significant Figures Significant Figures Notes – Physical Science**

1. Significant figures apply to measured values. They are significant to the measurement NOT to the number. 2. The number of significant figures is determined by the resolution of the instrument used to make the measurement. The last digit in a measured number is always the “estimated” digit.

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**Rules for Counting Significant Figures**

Non-zero numbers are ALWAYS significant. Example: 312cm and 0.546mm both have ______ significant figures 3

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**Sig. Fig. Rules - continued**

Leading Zeros are NEVER significant. Example: pm has _____ significant figures. consider this number in scientific notation: 4.7 x 10-5 How many significant figures? 2

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**Sig. Fig. Rules - continued**

Captured Zeros , zeros between two non zero numbers, are ALWAYS significant. Example: Both 4,005km and 40.05dm contain ______ significant figures. 4

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**Sig. Fig. Rules - continued**

Trailing Zeros are only significant if they are present with a decimal place. Example: 120mL has _____ sig. figs. 120.0mL has _____ sig. figs. Which number was measured with the more accurate volumetric measuring device? 2 4

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**Sig. Fig. Rules - continued**

Significant figures DO NOT APPLY to “counted” or “exact” numbers or definitions. Examples: 1 inch = 2.54 cm has NO sig. Fig. 14 pencils has NO sig figs. You do not use these numbers to determine the number of sig figs in your answer

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**Significant Figures Rules Summary**

Non-zero numbers – Always Significant Captured zeros – Always Significant Leading zeros – Never Significant Trailing zeros – Only with a decimal Counted numbers – does not apply Numeric Definitions – does not apply

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Rounding Rules Rule 1 - if the remainder beyond the last digit to be reported is less than 5, drop the numbers past the last digit. Example: Rounding to one decimal place, the number becomes 5.3. Rule 2 - if the remainder is equal or greater than 5, increase the final digit by 1. Example: The number becomes 5.8 if rounding to 2 digits. 4.025 becomes 4.03 if rounding to 3 digits.

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**Multiplying/Dividing with Significant Figures:**

The answer will have the same number of sig figs as the number with the least sig. figs in the calculation. Example: 30 x 5.1 = _______ BUT: 30 has only ____ sig fig so the answer can only have _____ sig fig. The correct answer is _____ 153 1 1 200

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**Adding/Subtracting with Significant Figures**

The answer will have the same number of decimal places as the number with the least decimal places in the calculation. Example: = ___________ BUT 3.2 has only one decimal place so the rounded answer is ______ 334.54 334.5

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**Practice – How many significant figures?**

46 marbles 3.02 x 102 cm in. 230 mL 2.4cm x 3.21cm 5.66mL mL 6.02 x 1023 atoms None 3 4 2 2 3 None

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