8 CHAPTER R Review of Basic Concepts Multiplying and Dividing by Powers of 10 (Shortcuts) • To multiply by a power of 10, move the decimal point to the right as many places as the number of zeros. • To divide by a power of 10, move the decimal point to the left as many places as the number of zeros. In both cases, insert 0s as placeholders if necessary. EXAMPLE 9 Multiplying and Dividing Decimals Multiply or divide as indicated. In part (c), round the answer to two decimal places. (a) 29.3 * 4.52 (b) 0.05 * 0.3 (c) 8.949 , 1.25 SOLUTION (a) Multiply normally. Place the decimal point in the answer as shown. 29.3 * 4.52 586 1465 1172 132.436 (b) Here 5 * 3 = 15. Be careful placing the decimal point. 2 decimal places 1 decimal place 0.05 * 0.3 = 0.015 1 decimal place 2 decimal places 1 + 2 = 3 3 decimal places 2 + 1 = 3 decimal places Attach 0 as a placeholder in the tenths place. Do not write 0.150. (c) 1.25 )8.949 Move each decimal point two places to the right. 7.159 125)894.900 875 199 125 740 625 1150 1125 25 Move the decimal point straight up, and divide as with whole numbers. Attach 0s as placeholders. We carried out the division to three decimal places so that we could round the answer to two decimal places, obtaining 7.16. S Now Try Exercises 105 and 113. NOTE To round 7.159 in Example 9(c) to two decimal places (that is, to the nearest hundredth), we look at the digit to the right of the hundredths place. • If this digit is 5 or greater, we round up. • If this digit is less than 5, we drop the digit(s) beyond the desired place. Hundredths place 7.159 9, the digit to the right of the hundredths place, is 5 or greater. ≈ 7.16 Round 5 up to 6. ≈ means is approximately equal to.
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