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Fractions
How do you convert a decimal to a fraction?
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2 Replies
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To convert a decimal to a fraction, follow these steps:
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Write the Decimal as a Fraction: Place the decimal number over 1 (e.g., 0.75 becomes 0.75/1).
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Eliminate the Decimal Point: Multiply both the numerator and the denominator by 10 for each digit after the decimal point. For example, to convert 0.75, multiply by 100 to get 75/100.
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Simplify the Fraction: Find the greatest common divisor (GCD) of the numerator and the denominator and divide both by this number. For 75/100, the GCD is 25, so divide both the numerator and denominator by 25 to get 3/4.
So, 0.75 as a fraction is 3/4.
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To convert a decimal to a fraction, you can follow these steps:
Identify the decimal point:
The digits to the left of the decimal point represent the whole number portion.
The digits to the right of the decimal point represent the fractional portion.
Identify the place value of the rightmost digit:
The rightmost digit in the fractional portion represents the denominator of the fraction.
For example, in the decimal 0.375, the rightmost digit is 5, so the denominator of the fraction will be 10^1 = 10.
Multiply the decimal by the appropriate power of 10:
Multiply the decimal by the power of 10 that corresponds to the rightmost digit’s place value.
This will move the decimal point to the right, leaving only whole numbers.
In the example, 0.375 × 10^2 = 37.5.
Write the result as a fraction:
The whole number portion becomes the numerator, and the power of 10 used becomes the denominator.
In the example, 37.5 becomes 37/5.
Simplify the fraction (optional):
If the fraction can be reduced, do so by finding the greatest common factor between the numerator and denominator, and dividing both by that factor.
In the example, 37/5 can be simplified to 7/1.
Here are some examples:
Convert 0.75 to a fraction:
The rightmost digit is 5, so the denominator is 10^1 = 10.
0.75 × 10 = 7.5
The fraction is 7/10, which can be simplified to 3/4.
Convert 0.375 to a fraction:
The rightmost digit is 5, so the denominator is 10^1 = 10.
0.375 × 10 = 3.75
The fraction is 3/10.
Convert 0.0625 to a fraction:
The rightmost digit is 5, so the denominator is 10^1 = 10.
0.0625 × 10 = 0.625
The fraction is 5/100, which can be simplified to 1/16.
The key is to understand the relationship between the decimal places and the denominator of the fraction. By applying this approach, you can convert any decimal to a fraction.
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