Multiplying and dividing by 10, 100, and 1000
Multiply and divide whole numbers and those involving decimals by 10, 100, and 1000
What a learner can do afterwards
- Calculate 3.45 × 100 = 345
- Calculate 72 ÷ 1000 = 0.072
- Explain that multiplying by 10 shifts each digit one place to the left
1 · Read
You already know that multiplying by 10 moves each digit one place to the left in the place-value chart. Multiplying by 100 moves every digit two places to the left, and multiplying by 1000 moves every digit three places to the left. This same rule works for decimal numbers, not just whole numbers.
To multiply 3.45 by 100, move every digit two places to the left in the place-value chart. The 3 moves into the hundreds place, the 4 moves into the tens place, and the 5 moves into the ones place. The digits line up as 345.
To divide 72 by 1000, move every digit three places to the right instead. The 7 moves into the hundredths place and the 2 moves into the thousandths place. The empty places get filled with zero, so 72 divided by 1000 equals 0.072.
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.
Multiplying shifts digits left and dividing shifts digits right, by as many places as the zeros in 10, 100, or 1000.
More to read
Multiplying decimals by 10, 100, and 1000
Multiplying by 100 shifts every digit two places to the left. So 3.45 x 100 = 345. The digits stay in the same order, but each one becomes worth a hundred times more. Thinking in jumps of place value beats counting zeros. Test it: 6.7 x 100 = 670, since 6 ones become 6 hundreds.
Dividing decimals by 10, 100, and 1000
Dividing by 1000 shifts every digit three places to the right. So 72 / 1000 = 0.072. Zeros hold the empty places so each digit lands in its correct column. A common slip is moving the digits the wrong number of places. Count the zeros in 1000: three zeros means three places.
Decimal place value review
Place value tells you what multiplication by 10 really does. Multiplying by 10 moves each digit one place to the left, which makes every digit worth ten times more. Dividing by 10 moves each digit one place to the right. Once you see the shift, sums like 450 / 10 = 45 and 0.9 x 1000 = 900 take seconds.
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Where it sits
17 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.