What is dectofrac 0.825 ?

The solution to dectofrac 0.825 is 33/40

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Popular >

Convert to a Simplified Fraction 0.825

Solution

decimal to fraction

0.825

Solution

\frac{33}{40}

Solution steps

0.825

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{0.825 \cdot 1000}{1000}

= \frac{825}{1000}

Reduce the fraction

\frac{825}{1000} : \frac{33}{40}

\frac{825}{1000}

Find a common factor of

825

and

1000

in order to cancel it out

Greatest Common Divisor of

825, 1000 : 25

825, 1000

Greatest Common Divisor (GCD)

Prime factorization of

825 : 3 \cdot 5 \cdot 5 \cdot 11

825

825

divides by

3825 = 275 \cdot 3

= 3 \cdot 275

275

divides by

5275 = 55 \cdot 5

= 3 \cdot 5 \cdot 55

55

divides by

555 = 11 \cdot 5

= 3 \cdot 5 \cdot 5 \cdot 11

3, 5, 11

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 5 \cdot 5 \cdot 11

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

825, 1000

are

= 5 \cdot 5

Multiply the numbers:

5 \cdot 5 = 25

= 25

Factor out

25

from the numerator and the denominator

825 = 25 \cdot 33, 1000 = 25 \cdot 40

= \frac{25 \cdot 33}{25 \cdot 40}

Cancel the common factor:

25

= \frac{33}{40}

= \frac{33}{40}

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Frequently Asked Questions (FAQ)

What is dectofrac 0.825 ?
The solution to dectofrac 0.825 is 33/40