Multiplying and Dividing by Powers of 10 (10, 100, 1000 and So
STRAND: Number TOPIC: Decimal numbers Multiplying and dividing by powers of 10 (10, 100, 1000 and so on) To multiply a whole number by a power of 10, add as many zeros to that number as there are in the power of 10. For example, to multiply by 10, add one zero and to multiply by 100, add two zeros. To multiply a decimal number by a power of 10, move the decimal point to the right one place for each zero in the power of 10. For example, to multiply by 10 move the decimal point one place to the right, while to multiply by 1000 move it three places to the right. Note that if there are not enough digits after the decimal point, we can always add extra zeros. WORKED Example 1 Calculate each of the following. a 72 × 10 b 540 × 1000 c 5.67 × 10 d 0.7 × 100 THINK WRITE a To multiply a whole number by 10, add one 0 a 72 × 10 = 720 to the number, as there is only one zero in 10.
b To multiply a whole number by 1000, add b 540 × 1000 = 540 000 three zeros, since there are 3 zeros in 1000.
c To multiply a decimal number by 10, move the c 5.67 × 10 = 56.7 decimal point one place to the right (as there is one zero in 10).
d To multiply a decimal number by 100, we need d 0.7 × 100 to move the decimal point two places to the = 0.70 × 100 right. However there is only one digit after the = 70 decimal point (7). So add a zero first (to create two decimal places), then move the decimal point. Note that we write the answer as 70, rather than 070.
To divide a whole or a decimal number by a power of 10, move the decimal point to the left one place for each zero in the power of 10. Note that although a whole number does not have a decimal point, we can always add it at the end of the number. (For example, 35 and 35 are the same numbers.) Also note that if there are not enough digits to move the decimal point the required number of places, we can always add extra zeros.
John Wiley & Sons Australia, Ltd 2001 STRAND: Number SKILLBUILDER: Multiplying and TOPIC: Decimal numbers dividing by powers of 10 (10, 100, 1000 and so on)
WORKED Example 2 Calculate each of the following. a 234 ÷ 100 b 350 ÷ 1000 c 75.6 ÷ 10 d 4.1 ÷ 1000 THINK WRITE
a 1 Put a decimal point at the end of the whole a 234 ÷ 100 = 234. ÷ 100 number. 2 To divide by 100, move the decimal point 2 234 ÷ 100 = 2.34 places to the left, as there are 2 zeros in 100.
b 1 Put a decimal point at the end of the whole b 350 ÷ 1000 = 350. ÷ 1000 number. 2 There are 3 zeros in 1000, so to divide by 234 ÷ 100 = 0.350 1000 move the decimal point 3 places to 234 ÷ 100 = 0.35 the left. You may wish to rewrite your answer, omitting the zero at the end of the resulting decimal (as 0.350 = 0.35).
c To divide by 10, move the decimal point one c 75.6 ÷ 10 = 7.56 place to the left (as there is 1 zero in 10).
d To divide by 1000, move the decimal point 3 d 4.1 ÷ 1000 = 0.0041 places to the left, since there are 3 zeros in 1000. (Add two extra zeros in front of the number 4.)
Try these 1 Calculate each of the following. a 23 × 10 b 45 × 10 c 235 × 10 d 530 × 10 e 2500 × 10 f 71 × 100 g 531 × 100 h 300 × 100 i 25 × 1000 j 710 × 1000 k 2 × 10 000 l 70 × 10 000 2 Calculate each of the following. a 2.56 × 10 b 7.6 × 10 c 0.98 × 10 d 3.49 × 100 e 2.6 × 100 f 70.1 × 100 g 0.2 × 100 h 5.321 × 1000 i 10.2 × 1000 j 0.758 × 1000 k 2.5 × 10 000 l 3.576 × 10 000 3 Calculate each of the following. a 128 ÷ 10 b 7560 ÷ 10 c 3400 ÷ 10 d 2050 ÷ 10 e 15 ÷ 100 f 7 ÷ 100 g 560 ÷ 100 h 7210 ÷ 100 i 3 ÷ 1000 j 75 ÷ 1000 k 600 ÷ 1000 l 2500 ÷ 10 000 4 Calculate each of the following. a 9.2 ÷ 10 b 52.3 ÷ 10 c 0.5 ÷ 10 d 8.19 ÷ 100 e 4.9 ÷ 100 f 123.4 ÷ 100 g 0.3 ÷ 100 h 71.1 ÷ 1000 i 155.6 ÷ 1000 j 4.25 ÷ 1000 k 75.3 ÷ 10 000 l 1000.5 ÷ 10 000
John Wiley & Sons Australia, Ltd 2001