Understanding 0.015625 as a Fraction
Have you ever come across the decimal 0.015625 and wondered how to express it as a fraction? It might seem daunting at first, but it's actually a simple process. This article will guide you through the steps of converting 0.015625 into a fraction.
What does 0.015625 represent?
0.015625 represents a part of a whole. It is a decimal, meaning it is a fraction where the denominator is a power of ten. However, expressing it as a fraction with a smaller denominator can be more convenient in certain situations.
Step-by-Step Conversion
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Write the decimal as a fraction with a denominator of 1:
0.015625 = 0.015625/1
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Multiply both numerator and denominator by 10 until the decimal point is removed:
Since there are 6 digits after the decimal point, we need to multiply by 10^6 (1,000,000) to remove the decimal.
(0.015625 * 1,000,000) / (1 * 1,000,000) = 15625/1000000
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Simplify the fraction by finding the greatest common factor (GCD):
The GCD of 15625 and 1000000 is 15625. Divide both numerator and denominator by 15625:
15625 / 15625 = 1 1000000 / 15625 = 64
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The final fraction is 1/64
Therefore, 0.015625 can be expressed as the fraction 1/64.
Using Powers of Two
Another way to understand this conversion is by recognizing that 0.015625 is equivalent to 1/2^6.
- 1/2 = 0.5
- 1/2^2 = 1/4 = 0.25
- 1/2^3 = 1/8 = 0.125
- 1/2^4 = 1/16 = 0.0625
- 1/2^5 = 1/32 = 0.03125
- 1/2^6 = 1/64 = 0.015625
This shows that 0.015625 is a power of two, which can be useful in certain contexts.
Conclusion
Converting 0.015625 to a fraction involves understanding how decimals represent parts of a whole and using appropriate mathematical operations to simplify the resulting fraction. The final fraction 1/64 can be used interchangeably with the decimal value, depending on the context and the desired level of precision.