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## Significant Figures

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**Uncertainty in Measurement**• The numbers reported in a measurement are limited by the measuring tool • Significant figures in a measurement include the known digits plus one estimated, or uncertain digit**This nail is 6.3 centimeters long for sure, but what exactly**is the value of the hundredths place – 6.35, 6.36, 6.37?**“Significant figures in a measurement consist of all the**digits known with certainty plus one final digit, which is somewhat uncertain or is estimated.” In the nail example, the hundredths place (3.36, the 6) is uncertain, or estimated. A SIGNIFICANT FIGURE IS NOT ALWAYS CERTAIN – THE LAST DIGIT OF ANY MEASUREMENT IS ESTIMATED!!!**Rules For Significant Figures**• All non-zero digits are significant Examples: 35 2 significant figures 48.96 4 significant figures**How many significant figures in 896.76**A. 2 B. 3 C. 4 D. 5**Rules For Significant Figures**2) Zeros between numbers (sandwiched zeros) are all significant Example: 304 – 3 significant digits 56.098 – 5 significant digits**How many significant figures in 1,043?**• 1 • 2 • 3 • 4**Rules For Significant Figures**3) Any zero appearing in front of a non-zero digit is NOT significant (regardless of a decimal) Example: 0.876 – 3 significant digits 0.0056 – 2 significant digits**How many significant figures in 0.0008**• 1 • 3 • 4 • 5**Rules for significant figures**4) Zeros at the end of a number AND to the right of a decimal point are significant Examples: 72.00 – 4 significant figures 7.000000000 – 10 significant figures**How many significant figures in 5.6000**• 2 • 4 • 5 • Help, I’m confused!**Rules For Significant Figures**5. A) Zeros at the end of the number WITHOUT a decimal place are NOT significant. Example: 3,000 – 1 significant figure 560 – 2 significant figures**How many significant figures does 453,000 have?**• 2 • 3 • 4 • 6**Rules For Significant Figures**5 B) Zeros at the end of a number to the LEFT of a decimal point are significant Example: • - Has three significant figures 4,000. – Has four significant figures**How many significant figures does 1,000. have?**• 1 • 2 • 3 • 4**How many sig figs does 305.00 have?**• 2 • 3 • 5 • Help! I’m confused!**How many sig figs does 0.009 have?**• 1 • 2 • 3 • 4**How many sig figs does 5,600.**• 1 • 2 • 3 • 4**Sig Figs in Calculations**• A calculated answer cannot be more precise than the measuring tool. • A calculated answer must match the least precise measurement. • Significant figures are needed for final answers from 1) adding or subtracting 2) multiplying or dividing**Sig Figs and Addition/Subtraction**The answer has the same number of decimal places as the measurement with the fewest decimal places. 25.2 one decimal place + 1.34two decimal places 26.54 answer 26.5 one decimal place**Round the answer to the correct number of significant**figures 235.05 + 19.6 + 2.1 = • 256.75 • 256.8 • 257**Round the answer to the correct number of significant**figures 58.925 - 18.2 • 40.725 • 40.73 • 40.7**Multiplying and Dividing with Sig Figs**Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.**2.19 X 4.2**• 9 • 9.2 • 9.198**4.311 ÷ 0.07**• 61.58 • 62 • 60