When multiplying and dividing decimals by powers of 10 greater than 1, you need to place decimal points in the correct position based on the number of zeros in the power of 10.
Here's how it works:
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Multiplying by Powers of 10: When you multiply a decimal by 10, 100, 1000, etc., you move the decimal point to the right. The number of places you move the decimal point corresponds to the number of zeros in the power of 10. For example:
- 3.25 × 10 = 32.5 (move the decimal point one place to the right)
- 4.6 × 100 = 460 (move the decimal point two places to the right)
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Dividing by Powers of 10: When you divide a decimal by 10, 100, 1000, etc., you move the decimal point to the left. Again, the number of places you move corresponds to the number of zeros in the power of 10. For example:
- 5.75 ÷ 10 = 0.575 (move the decimal point one place to the left)
- 8.4 ÷ 100 = 0.084 (move the decimal point two places to the left)
In summary, when multiplying, move the decimal point to the right, and when dividing, move it to the left.
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