What is dectofrac 0.525 ?

The solution to dectofrac 0.525 is 21/40

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Popular >

Convert to a Simplified Fraction 0.525

Solution

decimal to fraction

0.525

Solution

\frac{21}{40}

Solution steps

0.525

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{0.525 \cdot 1000}{1000}

= \frac{525}{1000}

Reduce the fraction

\frac{525}{1000} : \frac{21}{40}

\frac{525}{1000}

Find a common factor of

525

and

1000

in order to cancel it out

Greatest Common Divisor of

525, 1000 : 25

525, 1000

Greatest Common Divisor (GCD)

Prime factorization of

525 : 3 \cdot 5 \cdot 5 \cdot 7

525

525

divides by

3525 = 175 \cdot 3

= 3 \cdot 175

175

divides by

5175 = 35 \cdot 5

= 3 \cdot 5 \cdot 35

35

divides by

535 = 7 \cdot 5

= 3 \cdot 5 \cdot 5 \cdot 7

3, 5, 7

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 5 \cdot 5 \cdot 7

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

525, 1000

are

= 5 \cdot 5

Multiply the numbers:

5 \cdot 5 = 25

= 25

Factor out

25

from the numerator and the denominator

525 = 25 \cdot 21, 1000 = 25 \cdot 40

= \frac{25 \cdot 21}{25 \cdot 40}

Cancel the common factor:

25

= \frac{21}{40}

= \frac{21}{40}

Popular Examples

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35, 14

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39, 6

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ro u n d t o t h e n e a res t t e n t h 43.98

Divide 50/1.5 long division

\frac{50}{1.5}

Simplify 18/35

\frac{18}{35}

Frequently Asked Questions (FAQ)

What is dectofrac 0.525 ?
The solution to dectofrac 0.525 is 21/40