What is dectofrac 0.045 ?

The solution to dectofrac 0.045 is 9/200

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Popular >

Convert to a Simplified Fraction 0.045

Solution

decimal to fraction

0.045

Solution

\frac{9}{200}

Solution steps

0.045

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{0.045 \cdot 1000}{1000}

= \frac{45}{1000}

Reduce the fraction

\frac{45}{1000} : \frac{9}{200}

\frac{45}{1000}

Find a common factor of

45

and

1000

in order to cancel it out

Greatest Common Divisor of

45, 1000 : 5

45, 1000

Greatest Common Divisor (GCD)

Prime factorization of

45 : 3 \cdot 3 \cdot 5

45

45

divides by

345 = 15 \cdot 3

= 3 \cdot 15

15

divides by

315 = 5 \cdot 3

= 3 \cdot 3 \cdot 5

3, 5

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 3 \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

45, 1000

are

= 5

Factor out

5

from the numerator and the denominator

45 = 5 \cdot 9, 1000 = 5 \cdot 200

= \frac{5 \cdot 9}{5 \cdot 200}

Cancel the common factor:

5

= \frac{9}{200}

= \frac{9}{200}

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t h e \frac{80}{39}

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t h e \frac{144}{180}

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ro u n d t o t h e n e a res t h u n d re d t h 28.26

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13 \cdot 14

Divide Using Long Division 27/9 long division

\frac{27}{9}

Frequently Asked Questions (FAQ)

What is dectofrac 0.045 ?
The solution to dectofrac 0.045 is 9/200