MULTIPLYING NUMBERS BY 10, 100, 1000 - 1
Rule 1: To multiply a number by 10, 100, or 1000, move the decimal point in that number to the right as many places as there are zeros in the multiplier, attaching zeros if needed to make the required places.
When we multiply a number by a power of ten, we move the decimal point to the ______________
(right/left) as many places as there are _______________ in the power of ten.
Apply this rule to the following problems without actually doing the multiplication.
| 1) 7.74 × 10,000 | = ____________ | 13) 5.1 × 100,000 | = ____________ |
| 2) 25.9 × 100 | = ____________ | 14) 5.61 × 1,000 | = ____________ |
| 3) 8.7 × 10 | = ____________ | 15) 1.2 × 1,000,000 | = ____________ |
| 4) 82 × 100 | = ____________ | 16) 8.64 × 1,000 | = ____________ |
| 5) 19.3 × 100,000 | = ____________ | 17) 8.1 × 100 | = ____________ |
| 6) 28 × 10 | = ____________ | 18) 4 × 1,000 | = ____________ |
| 7) 1.112 × 10,000 | = ____________ | 19) 3.18 × 1,000 | = ____________ |
| 8) 7.1 × 1,000,000 | = ____________ | 20) 1.25 × 100 | = ____________ |
| 9) 39.5 × 100,000 | = ____________ | 21) 0.771 × 10 | = ____________ |
| 10) 59.8 × 10 | = ____________ | 22) 0.34 × 1000 | = ____________ |
| 11) 1.1 × 10,000 | = ____________ | 23) 1.01 × 10 | = ____________ |
| 12) 9.56 × 1,000 | = ____________ | 24) 0.99 × 10 | = ____________ |
25) When we move a decimal point four places to the right,
we _______________________
(multiply/divide) a number by _________________________.
26) Instead of using long multiplication, you can multiply
a number by 100 by moving the
decimal point _______________ (how many) places to the _______________
(right/left).
27) When we move the decimal point two places to the
right, we _______________
(multiply/divide) a number by _______________.
28) Instead of using long multiplication, you can multiply
a number by 10,000 by moving the
decimal point _______________ (how many) places to the _______________
(right/left).
RULE: RIGHT / ZEROS
| 1) 77,400 | 5) 1,930,000 | 9) 3,950,000 | 13) 510,000 | 17) 810 | 21) 7.71 | 25) MULTIPLY/10,000 |
| 2) 2,590 | 6) 280 | 10) 598 | 14) 5,610 | 18) 4,000 | 22) 340 | 26) TWO/RIGHT |
| 3) 87 | 7) 11,120 | 11) 11,000 | 15) 1,200,000 | 19) 3,180 | 23) 10.1 | 27) MULTIPLY/100 |
| 4) 8,200 | 8) 7,100,000 | 12) 9,560 | 16) 8,640 | 20) 125 | 24) 9.9 | 28) FOUR/RIGHT |
Rule 2: To divide a number by 10, 100, or 1000, move the decimal point in that number to the left as many places as there are zeros in the divisor, attaching zeros if needed to make the required places.
When we divide a number by a power of ten we move the decimal point to the _______________
(right/left) as many places as there are _______________ in the power of ten.
Apply this rule to the following problems without actually doing the division.
| 1) 2700 ÷ 10,000 | = ____________ | 13) 783.5 ÷ 10,000 | = ____________ |
| 2) 5164 ÷ 10 | = ____________ | 14) 98 ÷ 1,000,000 | = ____________ |
| 3) 0.31 ÷ 100,000 | = ____________ | 15) 2000 ÷ 1000 | = ____________ |
| 4) 20.8 ÷ 100 | = ____________ | 16) 12,583 ÷ 1000 | = ____________ |
| 5) 28.6 ÷ 100 | = ____________ | 17) 9.4 ÷ 100 | = ____________ |
| 6) 0.34 ÷ 10,000 | = ____________ | 18) 23.06 ÷ 10,000 | = ____________ |
| 7) 0.009 ÷ 10,000 | = ____________ | 19) 36 ÷ 100 | = ____________ |
| 8) 4.03 ÷ 10 | = ____________ | 20) 0.3276 ÷ 100 | = ____________ |
| 9) 647 ÷ 100 | = ____________ | 21) 12.34 ÷ 10 | = ____________ |
| 10) 53 ÷ 100,000 | = ____________ | 22) 385 ÷ 10 | = ____________ |
| 11) 9354 ÷ 100,000 | = ____________ | 23) 453.612 ÷ 1000 | = ____________ |
| 12) 0.4 ÷ 10 | = ____________ | 24) 3.18 ÷1000 | = ____________ |
25) When we move a decimal point four places to the left,
we _______________
(multiply/divide) a number by ______________.
26) Instead of using long division, you can divide a number by 1000 by moving the decimal point _______________ (how many) places to the _______________ (right/left).
27) When we move the decimal point five places to the
left, we _______________
(multiply/divide) a number by _______________.
28) Instead of using long division, you can divide a number by 100 by moving the decimal point _______________ (how many) places to the _______________ (right/left).
RULE: LEFT/ZEROS
| 1) 0.27 | 5) 0.286 | 9) 6.47 | 13) 0.07835 | 17) 0.094 | 21) 1.234 | 25) DIVIDE/10,000 |
| 2) 516.4 | 6) 0.000034 | 10) 0.00053 | 14) 0.000098 | 18) 0.002306 | 22) 38.5 | 26) THREE/LEFT |
| 3) 0.0000031 | 7) 0.0000009 | 11) 0.09354 | 15) 2 | 19) 0.36 | 23) 0.453612 | 27) DIVIDE/100,000 |
| 4) 0.208 | 8) 0.403 | 12) 0.04 | 16) 12.583 | 20) 0.003276 | 24) 0.00318 | 28) TWO/LEFT |