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To multiply decimals by powers of 10, move the decimal point to the right by the number of zeros in the power of 10. For example, multiplying by 100 (102) shifts the decimal two places to the right.
Let's discuss this in detail.
Decimal numbers are numbers that include a whole number and a fractional part, separated by a decimal point. The fractional part is expressed in powers of ten, such as tenths, hundredths, etc.
Decimal numbers are widely used in everyday life, particularly in money, measurements, and percentages, as they provide a clear and precise way to represent non-whole quantities.
Steps to multiply decimals by powers of 10 are:
Step 1: Determine the power of 10 by which you want to multiply the decimal.
Step 2: Move the decimal point to the right by as many places as there are zeros in the power of 10.
Step 3: If there aren’t enough digits to move the decimal point the required number of places, add zeros to the right of the number.
Example 1: Multiplying 4.56 by 10.
Solution:
Power of 10: 10 (one zero)
Move the decimal one place to the right: 4.56 × 10 = 45.6
Example 2: Multiplying 0.789 by 100.
Solution:
Power of 10: 100 (two zeros)
Move the decimal two places to the right: 0.789 × 100 = 78.9.
Example 3: Multiplying 3.2 by 1000.
Solution:
Power of 10: 1000 (three zeros)
Move the decimal three places to the right: 3.2×1000 = 3200.
Example 4: Multiplying 0.045 by 10000.
Solution:
Power of 10: 10000 (four zeros)
Move the decimal four places to the right: 0.045 × 10000 = 4500.0
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