Multiply and divide numbers by 10, 100, and 1000 giving answers up to three decimal places, understanding that digits shift position in the place-value chart
You already know how to multiply, divide, and read decimal numbers. Here is a shortcut for 10, 100, and 1000: instead of working out the whole calculation, you shift every digit to a new place in the place-value chart. Multiply by 10, and digits shift one place left. Multiply by 100, two places left. Multiply by 1000, three places left.
To work out 3.456 x 100, shift every digit two places left, since 100 has two zeros. The 3 moves from the ones place to the hundreds place: 3.456 becomes 345.6.
To work out 45.2 divided by 1000, shift every digit three places right, since 1000 has three zeros. There are not enough digits, so you fill the empty places with zeros: 45.2 becomes 0.0452. To undo a division, multiply by the same number: the digits shift back the same number of places to the left.
Count the zeros in 10, 100, or 1000. That tells you how many places to shift. Multiplying shifts digits left and makes the number bigger. Dividing shifts digits right and makes the number smaller.
Count the zeros, then shift every digit that many places: left to multiply, right to divide.
Practice items adapted from WeBWorK Open Problem Library problems by Carl Yao (PCC) (CC BY-NC-SA 3.0).
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