Check the solution to "Please, can u convert 3.16 (6 repeating) to..."

Monique Henson

Answered question

2023-03-29

Please, can u convert 3.16 (6 repeating) to fraction.

Answer & Explanation

popunjati7z8a

Beginner2023-03-30Added 4 answers

To convert the decimal number

3.16 \overset{―}{6}

(with the repeating 6) to a fraction, we can follow these steps:
Let

x = 3.16 \overset{―}{6}

.
We can multiply both sides of the equation by a power of 10 to eliminate the repeating decimal part. Since there is one digit repeating after the decimal point, we multiply by 10:

10 x = 31.66 \overset{―}{6}

Next, we subtract the original equation from the multiplied equation to eliminate the repeating part:

10 x - x = 31.66 \overset{―}{6} - 3.16 \overset{―}{6}

Simplifying the equation, we get:

9 x = 28.5

Now, we can solve for

x

by dividing both sides of the equation by 9:

x = \frac{28.5}{9}

Simplifying the fraction, we have:

x = 3 \frac{1}{6}

Therefore, the decimal

3.16 \overset{―}{6}

is equal to the fraction

3 \frac{1}{6}

.
Hence, the answer is

3 \frac{1}{6}

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