What is dectofrac-0.065 ?

The solution to dectofrac-0.065 is -13/200

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Popular >

Convert to a Simplified Fraction -0.065

Solution

decimal to fraction

- 0.065

Solution

- \frac{13}{200}

Solution steps

- 0.065

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{0.065 \cdot 1000}{1000}

= - \frac{65}{1000}

Reduce the fraction

\frac{65}{1000} : \frac{13}{200}

\frac{65}{1000}

Find a common factor of

65

and

1000

in order to cancel it out

Greatest Common Divisor of

65, 1000 : 5

65, 1000

Greatest Common Divisor (GCD)

Prime factorization of

65 : 5 \cdot 13

65

65

divides by

565 = 13 \cdot 5

= 5 \cdot 13

5, 13

are all prime numbers, therefore no further factorization is possible

= 5 \cdot 13

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

65, 1000

are

= 5

Factor out

5

from the numerator and the denominator

65 = 5 \cdot 13, 1000 = 5 \cdot 200

= \frac{5 \cdot 13}{5 \cdot 200}

Cancel the common factor:

5

= \frac{13}{200}

= - \frac{13}{200}

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Frequently Asked Questions (FAQ)

What is dectofrac-0.065 ?
The solution to dectofrac-0.065 is -13/200