What is tofraction 0.3125 ?

The solution to tofraction 0.3125 is 5/16

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Popular Pre Algebra >

Convert to a Simplified Fraction 0.3125

Solution

convert to fraction

0.3125

Solution

\frac{5}{16}

Decimal

0.3125

Solution steps

0.3125

Multiply and divide by 10 for every number after the decimal point.

There are

4

digits to the right of the decimal point, therefore multiply and divide by

10000

= \frac{0.3125 \cdot 10000}{10000}

= \frac{3125}{10000}

Reduce the fraction

\frac{3125}{10000} : \frac{5}{16}

\frac{3125}{10000}

Find a common factor of

3125

and

10000

in order to cancel it out

Greatest Common Divisor of

3125, 10000 : 625

3125, 10000

Greatest Common Divisor (GCD)

Prime factorization of

3125 : 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5

3125

3125

divides by

53125 = 625 \cdot 5

= 5 \cdot 625

625

divides by

5625 = 125 \cdot 5

= 5 \cdot 5 \cdot 125

125

divides by

5125 = 25 \cdot 5

= 5 \cdot 5 \cdot 5 \cdot 25

25

divides by

525 = 5 \cdot 5

= 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5

Prime factorization of

10000 : 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5 \cdot 5

10000

10000

divides by

210000 = 5000 \cdot 2

= 2 \cdot 5000

5000

divides by

25000 = 2500 \cdot 2

= 2 \cdot 2 \cdot 2500

2500

divides by

22500 = 1250 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 1250

1250

divides by

21250 = 625 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 625

625

divides by

5625 = 125 \cdot 5

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 125

125

divides by

5125 = 25 \cdot 5

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 25

25

divides by

525 = 5 \cdot 5

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5 \cdot 5

The prime factors common to

3125, 10000

are

= 5 \cdot 5 \cdot 5 \cdot 5

Multiply the numbers:

5 \cdot 5 \cdot 5 \cdot 5 = 625

= 625

Factor out

625

from the numerator and the denominator

3125 = 625 \cdot 5, 10000 = 625 \cdot 16

= \frac{625 \cdot 5}{625 \cdot 16}

Cancel the common factor:

625

= \frac{5}{16}

= \frac{5}{16}

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Frequently Asked Questions (FAQ)

What is tofraction 0.3125 ?
The solution to tofraction 0.3125 is 5/16

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