What is dectofrac 0.675 ?

The solution to dectofrac 0.675 is 27/40

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Popular >

Convert to a Simplified Fraction 0.675

Solution

decimal to fraction

0.675

Solution

\frac{27}{40}

Solution steps

0.675

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{0.675 \cdot 1000}{1000}

= \frac{675}{1000}

Reduce the fraction

\frac{675}{1000} : \frac{27}{40}

\frac{675}{1000}

Find a common factor of

675

and

1000

in order to cancel it out

Greatest Common Divisor of

675, 1000 : 25

675, 1000

Greatest Common Divisor (GCD)

Prime factorization of

675 : 3 \cdot 3 \cdot 3 \cdot 5 \cdot 5

675

675

divides by

3675 = 225 \cdot 3

= 3 \cdot 225

225

divides by

3225 = 75 \cdot 3

= 3 \cdot 3 \cdot 75

75

divides by

375 = 25 \cdot 3

= 3 \cdot 3 \cdot 3 \cdot 25

25

divides by

525 = 5 \cdot 5

= 3 \cdot 3 \cdot 3 \cdot 5 \cdot 5

3, 5

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 3 \cdot 3 \cdot 5 \cdot 5

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

675, 1000

are

= 5 \cdot 5

Multiply the numbers:

5 \cdot 5 = 25

= 25

Factor out

25

from the numerator and the denominator

675 = 25 \cdot 27, 1000 = 25 \cdot 40

= \frac{25 \cdot 27}{25 \cdot 40}

Cancel the common factor:

25

= \frac{27}{40}

= \frac{27}{40}

Popular Examples

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\frac{256}{32}

75-40 long subtraction

75 - 40

162/3 long division

\frac{162}{3}

Convert to a Simplified Fraction 1.56 decimal to fraction

1.56

Convert to a Mixed Number 7/2 mixed number

\frac{7}{2}

Frequently Asked Questions (FAQ)

What is dectofrac 0.675 ?
The solution to dectofrac 0.675 is 27/40