Question

How to turn repeating decimals to fractions.

Answer 1

To convert a repeating decimal to a fraction, set the decimal equal to x, multiply both sides by 10, subtract the original equation from the new one, and then solve for x. This will yield the equivalent fraction.

Step-by-step explanation:

To convert a repeating decimal to a fraction, follow these simple steps:

1. Let x be equal to the repeating decimal. For instance, we have 0.333...
2. Form an equation that will allow us to get rid of the repeating part. We can multiply each side of the equation by 10, it will be 10x = 3.333...
3. Subtract the original equation from the new equation. This gives us 9x = 3.
4. Solve for x by dividing each side by 9. This results in x = 3/9, which simplifies to x = 1/3.

Therefore, the repeating decimal 0.333... is equivalent to the fraction 1/3. We used the principle of multiplying by powers of ten and subtracting equations to get our answer.

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