What is dectofrac 0.666 ?

The solution to dectofrac 0.666 is 333/500

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Popular >

Convert to a Simplified Fraction 0.666

Solution

decimal to fraction

0.666

Solution

\frac{333}{500}

Solution steps

0.666

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

There are

3

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

1000

= \frac{0.666 \cdot 1000}{1000}

= \frac{666}{1000}

Reduce the fraction

\frac{666}{1000} : \frac{333}{500}

\frac{666}{1000}

Find a common factor of

666

and

1000

in order to cancel it out

Greatest Common Divisor of

666, 1000 : 2

666, 1000

Greatest Common Divisor (GCD)

Prime factorization of

666 : 2 \cdot 3 \cdot 3 \cdot 37

666

666

divides by

2666 = 333 \cdot 2

= 2 \cdot 333

333

divides by

3333 = 111 \cdot 3

= 2 \cdot 3 \cdot 111

111

divides by

3111 = 37 \cdot 3

= 2 \cdot 3 \cdot 3 \cdot 37

2, 3, 37

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 3 \cdot 37

Prime factorization of

1000 : 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5

1000

1000

divides by

21000 = 500 \cdot 2

= 2 \cdot 500

500

divides by

2500 = 250 \cdot 2

= 2 \cdot 2 \cdot 250

250

divides by

2250 = 125 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 125

125

divides by

5125 = 25 \cdot 5

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

25

divides by

525 = 5 \cdot 5

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

2, 5

are all prime numbers, therefore no further factorization is possible

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

The prime factors common to

666, 1000

are

= 2

Factor out

2

from the numerator and the denominator

666 = 2 \cdot 333, 1000 = 2 \cdot 500

= \frac{2 \cdot 333}{2 \cdot 500}

Cancel the common factor:

2

= \frac{333}{500}

= \frac{333}{500}

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Frequently Asked Questions (FAQ)

What is dectofrac 0.666 ?
The solution to dectofrac 0.666 is 333/500