What is dectofrac 1.5625 ?

The solution to dectofrac 1.5625 is 1 9/16

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Convert to a Simplified Fraction 1.5625

Solution

decimal to fraction

1.5625

Solution

1 \frac{9}{16}

Solution steps

1.5625

Rewrite as

= 1 + 0.5625

Convert

0.5625

to a fraction:

\frac{9}{16}

0.5625

Multiply and divide by 10 for every number after the decimal point.

There are

4

digits to the right of the decimal point, therefore multiply and divide by

10000

= \frac{0.5625 \cdot 10000}{10000}

= \frac{5625}{10000}

Reduce the fraction

\frac{5625}{10000} : \frac{9}{16}

\frac{5625}{10000}

Find a common factor of

5625

and

10000

in order to cancel it out

Greatest Common Divisor of

5625, 10000 : 625

5625, 10000

Greatest Common Divisor (GCD)

Prime factorization of

5625 : 3 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5

5625

5625

divides by

35625 = 1875 \cdot 3

= 3 \cdot 1875

1875

divides by

31875 = 625 \cdot 3

= 3 \cdot 3 \cdot 625

625

divides by

5625 = 125 \cdot 5

= 3 \cdot 3 \cdot 5 \cdot 125

125

divides by

5125 = 25 \cdot 5

= 3 \cdot 3 \cdot 5 \cdot 5 \cdot 25

25

divides by

525 = 5 \cdot 5

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

3, 5

are all prime numbers, therefore no further factorization is possible

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

Prime factorization of

10000 : 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5 \cdot 5

10000

10000

divides by

210000 = 5000 \cdot 2

= 2 \cdot 5000

5000

divides by

25000 = 2500 \cdot 2

= 2 \cdot 2 \cdot 2500

2500

divides by

22500 = 1250 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 1250

1250

divides by

21250 = 625 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 625

625

divides by

5625 = 125 \cdot 5

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 125

125

divides by

5125 = 25 \cdot 5

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 25

25

divides by

525 = 5 \cdot 5

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5 \cdot 5

The prime factors common to

5625, 10000

are

= 5 \cdot 5 \cdot 5 \cdot 5

Multiply the numbers:

5 \cdot 5 \cdot 5 \cdot 5 = 625

= 625

Factor out

625

from the numerator and the denominator

5625 = 625 \cdot 9, 10000 = 625 \cdot 16

= \frac{625 \cdot 9}{625 \cdot 16}

Cancel the common factor:

625

= \frac{9}{16}

= \frac{9}{16}

= 1 + \frac{9}{16}

= 1 \frac{9}{16}

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\frac{5}{4}

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\frac{12}{9}

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\frac{34}{2}

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\frac{30}{8}

Frequently Asked Questions (FAQ)

What is dectofrac 1.5625 ?
The solution to dectofrac 1.5625 is 1 9/16