What is tofraction 0.1666 ?

The solution to tofraction 0.1666 is 833/5000

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Popular Pre Algebra >

Convert to a Simplified Fraction 0.1666

Solution

tofraction

Solution

\frac{833}{5000}

Decimal

0.1666

Solution steps

0.1666

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{0.1666 \cdot 10000}{10000}

= \frac{1666}{10000}

Reduce the fraction

\frac{1666}{10000} : \frac{833}{5000}

\frac{1666}{10000}

Find a common factor of

1666

and

10000

in order to cancel it out

Greatest Common Divisor of

1666, 10000 : 2

1666, 10000

Greatest Common Divisor (GCD)

Prime factorization of

1666 : 2 \cdot 7 \cdot 7 \cdot 17

1666

1666

divides by

21666 = 833 \cdot 2

= 2 \cdot 833

833

divides by

7833 = 119 \cdot 7

= 2 \cdot 7 \cdot 119

119

divides by

7119 = 17 \cdot 7

= 2 \cdot 7 \cdot 7 \cdot 17

2, 7, 17

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 7 \cdot 7 \cdot 17

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

1666, 10000

are

= 2

Factor out

2

from the numerator and the denominator

1666 = 2 \cdot 833, 10000 = 2 \cdot 5000

= \frac{2 \cdot 833}{2 \cdot 5000}

Cancel the common factor:

2

= \frac{833}{5000}

= \frac{833}{5000}

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Frequently Asked Questions (FAQ)

What is tofraction 0.1666 ?
The solution to tofraction 0.1666 is 833/5000

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