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Understanding Significant Digits in Measurements and Calculations

This article explains the concept of significant digits and their importance in representing measurements accurately. Significant digits include all known digits of a value plus one uncertain digit. Various rules guide the treatment of significant digits in different calculations, including addition, subtraction, multiplication, and division. By mastering these rules, students can ensure their answers reflect the precision of their measurements. Practical examples illustrate how to identify significant digits and correctly round results based on these rules.

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Understanding Significant Digits in Measurements and Calculations

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  1. What time is it? • Someone might say “1:30” or “1:28” or “1:27:55” • Each is appropriate for a different situation • In science we describe a value as having a certain number of “significant digits” • The # of significant digits in a value includes all digits that are certain and one that is uncertain • “1:30” likely has 2, 1:28 has 3, 1:27:55 has 5 • There are rules that dictate the # of significant digits in a value

  2. 12.6172 has 6 significant figures 1.7 has 2 significant figures Rules for Determining Significant Zeros

  3. Student Challenge. Identify the number of significant digits shown in each of the following examples. A) 259 B) 3500 C) 0.050090 D) 4.50 x 108 E) 0.004 F) 3500.

  4. Rule for Addition and Subtraction For addition and subtraction, your answer must show the same number of decimal places as the number in the calculation with the least number of decimal places. Rule for Multiplication and Division For multiplication and division, your answer must show the same number of significant digits as the measurement in the calculation with the least number of significant digits.

  5. Rule for Addition and Subtraction For example, 25.1 g + 2.03 g = 27.13 g 27.13 suggests that we can measure with certainty to the hundreths place. But the measurement of 25.1 says we don’t know that value with certainty to the hundredths place. So we must round down to 27.1 g.

  6. Rule for Multiplication and Division For example, 3.40 cm x 12.61 cm x 18.25 cm = 782.4505 cm3 before rounding We, can’t report an answer with seven significant digits if the measurement with the least number of significant digits in our calculation, 3.40 cm, shows only three significant digits. We must round our answer to three significant digits, giving us a rounded answer of 782 cm3.

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