Converting decimals to fractions can be a valuable skill for various applications, from solving mathematical problems to interpreting scientific data.
Several reasons exist for converting decimals to fractions:
Converting decimals to fractions involves two main steps:
Write the decimal as the numerator of a fraction over a denominator of 1.
Example: For the decimal 0.25,
0.25 = 25/100
Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD).
Example: For the fraction 25/100, the GCD is 25:
25/100 = (25 ÷ 25)/(100 ÷ 25) = 1/4
Decimals are closely related to percentages. A percentage represents a fraction of 100%. To convert a percentage to a fraction, simply divide the percentage by 100.
Example: To convert 50% to a fraction:
50% = 50/100 = 1/2
Some decimals repeat endlessly, known as repeating decimals. To convert a repeating decimal to a fraction, follow these steps:
Locate the block of digits that repeats.
Write the repeating block as the numerator and place it over a denominator of 9 repeated as many times as the length of the block.
Simplify the fraction by factoring common elements from the numerator and denominator.
Example: To convert the repeating decimal 0.333... to a fraction:
0.333... = 3/(9 * 3) = 1/9
Decimal | Fraction |
---|---|
0.5 | 1/2 |
0.25 | 1/4 |
0.75 | 3/4 |
0.125 | 1/8 |
0.666... | 1/3 |
Percentage | Fraction |
---|---|
50% | 1/2 |
25% | 1/4 |
75% | 3/4 |
12.5% | 1/8 |
33.333...% | 1/3 |
Repeating Decimal | Fraction |
---|---|
0.142857... | 1/7 |
0.272727... | 1/3 |
0.363636... | 1/2 |
0.454545... | 1/2 |
0.636363... | 3/5 |
Converting decimals to fractions is a valuable skill that enhances mathematical understanding and problem-solving abilities. By following the steps and strategies outlined in this article, you can effectively make these conversions and confidently use fractions in various applications.
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