# 1 Significant Digits Reflect the accuracy of the measurement and the precision of the measuring device. All the figures known with certainty plus one extra.

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1 Significant Digits Reflect the accuracy of the measurement and the precision of the measuring device. All the figures known with certainty plus one extra digit are called significant digits or figures.

2 Significant Digits Rules for Identifying the Number of Significant Digits. Non-zero numbers are always significant. Zeros found between non-zero numbers are always significant. Zeros to the right of both a decimal place and a significant digit are significant. Zeros that are used solely as placeholders are not considered significant.

3 Significant Digits Identify the number of significant digits shown in each of the following examples. A) 2593 significant digits. B) 3500 2 significant digits C) 0.050090 5 significant digits D) 4.50 x 10 8 3 significant digits E) 0.004 1 significant digit

4 Significant Digits 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 Significant Digits Rule for Multiplication and Division For example, 3.40 cm x 12.61 cm x 18.25 cm = 782.4505 cm 3 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 cm 3.

6 Significant Digits 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.

7 Significant Digits Rule for Addition and Subtraction For example, 22.530 m/s – 8.07 m/s = 14.46 m/s In this example, our answer would be correct as shown. The measurement with the least number of decimal places, 8.07 m/s, is reported to the hundredths place. Our answer must also be reported to the hundredth place as 14.46 m/s.

8 Significant Digits Use of Scientific Notation to Show the Proper Number of Significant Digits There will be times when you see answers that are written in scientific notation, and you might not be sure why. Often, answers are written in scientific notation just to express the answer in the correct number of significant digits.

9 Significant Digits Use of Scientific Notation to Show the Proper Number of Significant Digits Look at the following example. 8.0 m x 50.0 m = 400 m 2 The measurement in this calculation with the least number of significant digits, 8.0 m, shows two significant digits. Our answer only shows one significant digit. We can write this answer in scientific notation just for the purpose of showing the same value with two significant digits. Our answer would be expressed as 4.0 x 10 2 m 2.

10 Significant Digits Use of Scientific Notation to Show the Proper Number of Significant Digits Another method for showing additional significant digits involves using a decimal at the right of a significant digit of zero. For example, if you wanted to show the number 700 with three significant digits, you could put a decimal point to the right of the second zero, as in “700.” or you could use either of the other two methods described here.

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