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The smallest division is 10 mL, so we can read the volume to +/- 1/10 of 10 mL or +/- 1 mL.

The smallest division is 10 mL, so we can read the volume to +/- 1/10 of 10 mL or +/- 1 mL. The volume we read from the beaker has a reading error of +/- 1 mL. The volume in this beaker is 47 +/-1 mL. You might have read 46 mL; your friend might read the volume as 48 mL.

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The smallest division is 10 mL, so we can read the volume to +/- 1/10 of 10 mL or +/- 1 mL.

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  1. The smallest division is 10 mL, so we can read the volume to +/- 1/10 of 10 mL or +/- 1 mL. The volume we read from the beaker has a reading error of +/- 1 mL. The volume in this beaker is 47 +/-1 mL. You might have read 46 mL; your friend might read the volume as 48 mL. All the answers are correct within the reading error of +/-1 mL. So, How many significant figures does our volume of 47 +/- 1 mL have? Answer - 2! The "4" we know for sure plus the "7" we had to estimate.

  2. When we read the volume, we read it at the BOTTOM of the meniscus. The smallest division of this graduated cylinder is 1 mL. Therefore, our reading error will be +/- 0.1 mL or 1/10 of the smallest division. An appropriate reading of the volume is 36.5 +/- 0.1 mL. An equally precise value would be 36.6 mL or 36.4 mL. How many significant figures does our answer have? 3! The "3" and the "6" we know for sure and the "5" we had to estimate a little.

  3. The smallest division in this buret is 0.1 mL. Therefore, our reading error is +/- 0.01 mL. A good volume reading is 20.38 +/- 0.01 mL. An equally precise answer would be 20.39 mL or 20.37 mL. How many significant figures does our answer have? 4! The "2", "0", and "3" we definitely know and the "8" we had to estimate.

  4. Rules For Significant Digits • Digits from 1-9 are always significant. • Zeros between two other significant digits are always significant • One or more additional zeros to the right of both the decimal place and another significant digit are significant. • Zeros used solely for spacing the decimal point (placeholders) are not significant.

  5. Examples of Significant Digits

  6. Multiplying and Dividing RULE: When multiplying or dividing, your answer may only show as many significant digits as the multiplied or divided measurement showing the least number of significant digits.

  7. Example: When multiplying • 22.37 cm x 3.10 cm x 85.75 cm • = 5946.50525 cm3 • We look to the original problem and check the number of significant digits in each of the original measurements: • 22.37 shows 4 significant digits. • 3.10 shows 3 significant digits. • 85.75 shows 4 significant digits.

  8. Example: When multiplying • 22.37 cm x 3.10 cm x 85.75 cm • = 5946.50525 cm3 • Our answer can only show 3 significant digits because that is the least number of significant digits in the original problem. • 5946.50525 shows 9 significant digits • We must round to the tens place in order to show only 3 significant digits. • Our final answer becomes 5950 cm3.

  9. Adding and Subtracting RULE: When adding or subtracting your answer can only show as many decimal places as the measurement having the fewest number of decimal places.

  10. Example: When we add 3.76 g + 14.83 g + 2.1 g = 20.69 g We look to the original problem to see the number of decimal places shown in each of the original measurements. 2.1 shows the least number of decimal places. We must round our answer, 20.69, to one decimal place (the tenth place). Our final answer is 20.7 g

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