Movement of the Decimal Point
Decimal point movement multiplies or divides a number by powers of 10 like 10, 100 or 1000. Multiplying shifts the point right, making the number bigger. Dividing shifts it left, making the number smaller.
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Multiplying and Dividing by 10, 100, 1000
- Multiplying by 10, 100, 1000 moves the decimal right.
- Dividing by 10, 100, 1000 moves the decimal left.
How to Shift the Decimal Point
- Multiplying by 1000 means moving the decimal point 3 places to the right.
- Dividing by 100 means moving the decimal point 2 places to the left.
Using Decimal Movement to Convert Units
- When converting to smaller units, multiply by the conversion factor. For example,
- When converting to larger units, divide by the conversion factor. For example,
Practice Questions
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What is 7.3 multiplied by 10?
Correct! 🎉 +10 pointsNot quite right
Multiplying by 10 moves the decimal point one place to the right, so 7.3 becomes 73.
What is 0.5 multiplied by 1000?
Correct! 🎉 +10 pointsNot quite right
Multiplying by 1000 moves the decimal point three places to the right, so 0.5 becomes 500.
What is 8 divided by 100?
Correct! 🎉 +20 pointsNot quite right
Dividing by 100 moves the decimal point two places to the left, so 8 becomes 0.08.
Convert 8.9 metres into millimetres.
Correct! 🎉 +20 pointsNot quite right
Multiplying by 1000 moves the decimal point three places to the right, so 8.9 becomes 8900.
What is 78.4 divided by 1000?
Correct! 🎉 +20 pointsNot quite right
Dividing by 1000 moves the decimal point three places to the left, so 78.4 becomes 0.0784.
Convert and divide it by 10.
Correct! 🎉 +30 pointsNot quite right
First, convert to a decimal by dividing by 100, giving 0.125. Then divide by 10, moving the decimal one place to the left, resulting in 0.0125.
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Movement of the Decimal Point
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Students Also Ask
The questions students bump into most on this topic
Multiplying by 10 makes a number 10 times larger. Every digit then moves up one place-value column. The decimal point acts as a marker between the ones and the tenths. So when the digits shift one column to the left, the point appears to slide one place to the right.
A whole number has an invisible decimal point at the end. For example, 23 means 23. with the point after the units digit. You can write the point in before you move it. So 23 × 100 becomes 23. → 2300. The two empty places get filled with zeros.
Fill any empty places with zeros. If you divide 4.21 by 100, you need two more places. They go to the left of the digits. The answer becomes 0.0421. Zeros fill the gap, and a leading zero goes before the point.
Rewrite the percentage as a division by 100. Then move the decimal point 2 places to the left. So 56.7% becomes 56.7 ÷ 100 = 0.567. From there you can multiply again. For example, 0.567 × 10 = 5.67. That uses one more shift to the right.
Yes. Moving the point right makes the number larger. That happens because you are multiplying by a power of 10. Moving it left makes the number smaller. That happens because you are dividing by a power of 10. The direction of the move tells you which is happening.
Many metric units differ by powers of 10. To convert 2.8 m to cm, multiply by 100. Shift the decimal point 2 places right. The answer is 280 cm. To convert 2.8 m to km, divide by 1000. Shift the point 3 places left. The answer is 0.0028 km.