What is dectofrac 0.775 ?

The solution to dectofrac 0.775 is 31/40

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Popular >

Convert to a Simplified Fraction 0.775

Solution

decimal to fraction

0.775

Solution

\frac{31}{40}

Solution steps

0.775

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{0.775 \cdot 1000}{1000}

= \frac{775}{1000}

Reduce the fraction

\frac{775}{1000} : \frac{31}{40}

\frac{775}{1000}

Find a common factor of

775

and

1000

in order to cancel it out

Greatest Common Divisor of

775, 1000 : 25

775, 1000

Greatest Common Divisor (GCD)

Prime factorization of

775 : 5 \cdot 5 \cdot 31

775

775

divides by

5775 = 155 \cdot 5

= 5 \cdot 155

155

divides by

5155 = 31 \cdot 5

= 5 \cdot 5 \cdot 31

5, 31

are all prime numbers, therefore no further factorization is possible

= 5 \cdot 5 \cdot 31

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

775, 1000

are

= 5 \cdot 5

Multiply the numbers:

5 \cdot 5 = 25

= 25

Factor out

25

from the numerator and the denominator

775 = 25 \cdot 31, 1000 = 25 \cdot 40

= \frac{25 \cdot 31}{25 \cdot 40}

Cancel the common factor:

25

= \frac{31}{40}

= \frac{31}{40}

Popular Examples

Reduce the Fraction 36/66 reduce fraction

t h e \frac{36}{66}

2.5/6 long division

\frac{2.5}{6}

Write the Fraction in Simplest Form (7/6)÷3

(7/6) /3

Convert to a Mixed Number 7/12 mixed number

\frac{7}{12}

Find the LCM 9 , 8 , 4 lcm

9, 8, 4

Frequently Asked Questions (FAQ)

What is dectofrac 0.775 ?
The solution to dectofrac 0.775 is 31/40