Multiplying a decimal by a power of 10 involves shifting the decimal point to the right. The number of places to shift the decimal point is determined by the exponent of the power of 10. For example, multiplying a decimal by 10^2 (or 100) would shift the decimal point two places to the right.
Key Facts
- Multiplying a decimal by a power of 10 involves shifting the decimal point to the right. The number of places to shift the decimal point is determined by the exponent of the power of 10. For example, multiplying a decimal by 10^2 (or 100) would shift the decimal point two places to the right.
- When multiplying a decimal by a power of 10, the digits of the decimal remain the same, but their position changes. The value of the decimal does not change, only its representation. For example, multiplying 0.25 by 10^3 (or 1000) would result in 250.
- The number of zeros in the power of 10 determines the number of places the decimal point is shifted. For example, multiplying a decimal by 10^4 (or 10,000) would shift the decimal point four places to the right.
- It is important to remember that multiplying by a power of 10 does not change the value of the decimal, only its scale. The digits of the decimal remain the same, and the relative size of the digits remains unchanged.
Rules for Multiplying Decimals by Powers of 10
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Multiplying by 10^n
When multiplying a decimal by 10^n, the decimal point is shifted n places to the right. The digits of the decimal remain the same, but their position changes. The value of the decimal does not change, only its representation.
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Multiplying by 10^0
Multiplying a decimal by 10^0 is equivalent to multiplying by 1. The decimal point remains in its original position.
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Multiplying by 10^-n
When multiplying a decimal by 10^-n, the decimal point is shifted n places to the left. The digits of the decimal remain the same, but their position changes. The value of the decimal does not change, only its representation.
Examples of Multiplying Decimals by Powers of 10
- Multiplying 0.25 by 10^2
0.25 x 10^2 = 25
In this example, the decimal point is shifted two places to the right, resulting in the product 25.
- Multiplying 3.14 by 10^3
3.14 x 10^3 = 3140
In this example, the decimal point is shifted three places to the right, resulting in the product 3140.
- Multiplying 0.005 by 10^-2
0.005 x 10^-2 = 0.0005
In this example, the decimal point is shifted two places to the left, resulting in the product 0.0005.
Conclusion
Multiplying decimals by powers of 10 is a fundamental operation in mathematics. It is frequently used in various applications, including scientific calculations, financial transactions, and data analysis. Understanding the rules and procedures for multiplying decimals by powers of 10 is essential for performing accurate calculations and solving mathematical problems effectively.
References
- Multiplying Decimals by Powers of 10 — Rules & Examples – Expii
- Multiplying Decimals – Definition with Examples
- Multiplying a decimal by a power of 10 (video) | Khan Academy
FAQs
What is the rule for multiplying decimals by powers of 10?
When multiplying a decimal by a power of 10, the decimal point is shifted to the right by the number of zeros in the power of 10. The digits of the decimal remain the same.
What happens when you multiply a decimal by 10^n?
Multiplying a decimal by 10^n is equivalent to shifting the decimal point n places to the right. The value of the decimal does not change, only its representation.
What happens when you multiply a decimal by 10^0?
Multiplying a decimal by 10^0 is equivalent to multiplying by 1. The decimal point remains in its original position.
What happens when you multiply a decimal by 10^-n?
Multiplying a decimal by 10^-n is equivalent to shifting the decimal point n places to the left. The value of the decimal does not change, only its representation.
How do you multiply decimals by powers of 10 greater than 1?
To multiply a decimal by a power of 10 greater than 1, simply shift the decimal point to the right by the number of zeros in the power of 10.
How do you multiply decimals by powers of 10 less than 1?
To multiply a decimal by a power of 10 less than 1, simply shift the decimal point to the left by the number of zeros in the power of 10.
What is the significance of multiplying decimals by powers of 10?
Multiplying decimals by powers of 10 is a fundamental operation in mathematics and is frequently used in various applications, including scientific calculations, financial transactions, and data analysis.
How can I check if my answer is correct when multiplying decimals by powers of 10?
You can check the accuracy of your answer by performing the reverse operation. Divide the product by the power of 10 used for multiplication. If the result is the original decimal, then your answer is correct.