MULTIPLICATION AND DIVISION BY POWERS OF TEN Consider the two numbers, (a) 320.12, (b) 3,201.2. Both are expressed by the same figures written in the same order. The number (b) can be obtained from the number (a) by moving each figure one place to the left. But moving a digit one place to the left makes its value ten times as great, and, hence, moving several digits each one place to the left makes the number they represent ten times as great. The number (b) can also be obtained from (a) by moving the decimal point in (a) one place to the right. Also (a) can be obtained from (b) by moving the decimal point in (b) one place to the left. To multiply a number by 10, move the decimal point in the number one place to the right. To divide a number by 10, move the decimal point in the number one place to the left. Consider the numbers, (a) 320.12, The number (b) is obtained from (a) by moving each digit in (a) two places to the left. This multiplies each digit by 100. (b) may also be obtained from (a) by moving the decimal point in (a) two places to the right; also (a) from (b) by moving the decimal point two places to the left. To multiply a number by 100, move the decimal point in the number two places to the right. To divide by 100, move the decimal point in the dividend two places to the left. Consider the numbers, (a) 320.12, (b) 320,120. (b) is here obtained from (a) by moving each digit in (a) three places to the left. It can also be obtained from (a) by moving the decimal point in (a) three places to the right. To multiply a number by 1,000, move the decimal point in the number three places to the right. To divide a number by 1,000, move the decimal point in the number three places to the left. The rules for multiplying by 10,000, 100,000, are left for the reader to determine. Example 1. Multiply 86.4 by 10,000. Moving the decimal point four places to the right, the number becomes 864,000. Example 2. Divide 12.3 by 100,000. Moving the decimal point five places to the left, the number becomes .000123. EXERCISE 32 Multiply by 10: 1. 120, 14.2, .1431, .00012, 1.7320, .01234. Multiply by 100: 2. 173, 172.8, 19.23, .001237, 8,654, 17.1. Multiply by 1,000: 3. 1156, 32.5, 7.123, .93891, .01275, .00011. Multiply by 10,000: 4. 345, 34.25, 5.1739, 6.001, .01793, .12. 5. Divide each of the following numbers by 10; by 100; by 1,000; by 10,000; by 100,000: 22. .001: 10. 23. .005: 100. 24. 9.265: 926.5. 25. 12.325: 1,232.5. 26. 1.534: 153.4. 27. 1,001 .1001. 28. 54: .054. 29. 792: .0792. 30. 113.0113. 31. 79.28.7928. 32. 6.45: 6,450. 33. 99.29 99,290. 34. 7.35: 73,500. 35. 9.24 92,400. 36. 8.123: .008123. : 21. 11.79 11,790. 37. .04567 : 45.670. ADDITION Find the sum of 3.4, 2.38, 5.005, 6.2374, 11.1. 3.4 2.38 5.005 6.2374 11.1 Write the numbers so that units of the same denomination stand in the same vertical column. Then add as integers are added. Write the decimal point in the sum in the same vertical line with the decimal points in the 28.1224 addends. Add: EXERCISE 33 1. 2.2, .025, 37.3, 5.284, 6.294, 538.1, 77.77. SUBTRACTION Find the difference between 4,001 and 1.7003. 4001.0000 1.7003 Arrange the numbers so that units of the same denomination stand in the same vertical column. Ciphers may be inserted after the 3999.2997 decimal point in the minuend. Proceed next as in the subtraction of integers. 27. From seven hundred four thousandths take two hundred five ten-thousandths. 28. From five hundred ten thousandths take five hundred ten-thousandths. 29. From two thousand take two thousandths. 30. How much does one thousandth exceed one hundredthousandth? 31. Find the difference between a hundred and a hundredth. 32. From 39 tenths take 39 thousandths. 33. From 100 hundredths take 100 ten-thousandths. 34. How much must be added to one and five-tenths to make ten? |