Add and subtract decimals, then multiply and divide by multiples of powers of ten.
Example 1
What happens to the value of each digit when 9.67 is multiplied by 100?
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Answer: Each digit represents a value 100 times as large.
- Multiplication by 100 makes the entire number 100 times as large.
- The digits take place values two places to the left; their values increase by a factor of 100.
Example 2
Calculate 1.25×200 without a calculator.
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Answer: 250
- Use place value and multiplication facts.
- 1.25×200=250; multiplying by 200 makes the value 200 times as large.
- Check by rounding 1.25 to the nearest tenth: 1.3×200=260, a nearby estimate.
Example 3
What happens to the value of each digit when 6.74 is multiplied by 100?
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Answer: Each digit represents a value 100 times as large.
- Multiplication by 100 makes the entire number 100 times as large.
- The digits take place values two places to the left; their values increase by a factor of 100.