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.
What are Decimal Numbers?
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.
How to Multiply Decimals by Powers of 10?
Steps to multiply decimals by powers of 10 are:
Step 1: Determine the power of 10 by which you want to multiply the decimal.
- For example, if you are multiplying by 100, this is 102 or two powers of 10.
Step 2: Move the decimal point to the right by as many places as there are zeros in the power of 10.
- If multiplying by 10, move the decimal one place to the right.
- If multiplying by 100, move the decimal two places to the right.
- If multiplying by 1000, move the decimal three places to the right, and so on.
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 of Multiply Decimals by Powers of 10
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
Summary
- When you multiply a decimal by 10, move the decimal point one place to the right.
- When you multiply a decimal by 100, move the decimal point two places to the right.
- When you multiply a decimal by 1000, move the decimal point three places to the right, and so on.
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