What is dectofrac 0.512 ?

The solution to dectofrac 0.512 is 64/125

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Popular >

Convert to a Simplified Fraction 0.512

Solution

decimal to fraction

0.512

Solution

\frac{64}{125}

Solution steps

0.512

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{0.512 \cdot 1000}{1000}

= \frac{512}{1000}

Reduce the fraction

\frac{512}{1000} : \frac{64}{125}

\frac{512}{1000}

Find a common factor of

512

and

1000

in order to cancel it out

Greatest Common Divisor of

512, 1000 : 8

512, 1000

Greatest Common Divisor (GCD)

Prime factorization of

512 : 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2

512

512

divides by

2512 = 256 \cdot 2

= 2 \cdot 256

256

divides by

2256 = 128 \cdot 2

= 2 \cdot 2 \cdot 128

128

divides by

2128 = 64 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 64

64

divides by

264 = 32 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 32

32

divides by

232 = 16 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 16

16

divides by

216 = 8 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 4

4

divides by

24 = 2 \cdot 2

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

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

512, 1000

are

= 2 \cdot 2 \cdot 2

Multiply the numbers:

2 \cdot 2 \cdot 2 = 8

= 8

Factor out

8

from the numerator and the denominator

512 = 8 \cdot 64, 1000 = 8 \cdot 125

= \frac{8 \cdot 64}{8 \cdot 125}

Cancel the common factor:

8

= \frac{64}{125}

= \frac{64}{125}

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\frac{135}{120}

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\frac{9}{2}

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16 x y^{2} + 28 x y + 8 y

Divide 172/2 long division

\frac{172}{2}

1200*5 long multiplication

1200 \cdot 5

Frequently Asked Questions (FAQ)

What is dectofrac 0.512 ?
The solution to dectofrac 0.512 is 64/125