What is dectofrac 0.416 ?

The solution to dectofrac 0.416 is 52/125

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Popular >

Convert to a Simplified Fraction 0.416

Solution

decimal to fraction

0.416

Solution

\frac{52}{125}

Solution steps

0.416

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{0.416 \cdot 1000}{1000}

= \frac{416}{1000}

Reduce the fraction

\frac{416}{1000} : \frac{52}{125}

\frac{416}{1000}

Find a common factor of

416

and

1000

in order to cancel it out

Greatest Common Divisor of

416, 1000 : 8

416, 1000

Greatest Common Divisor (GCD)

Prime factorization of

416 : 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 13

416

416

divides by

2416 = 208 \cdot 2

= 2 \cdot 208

208

divides by

2208 = 104 \cdot 2

= 2 \cdot 2 \cdot 104

104

divides by

2104 = 52 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 52

52

divides by

252 = 26 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 26

26

divides by

226 = 13 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 13

2, 13

are all prime numbers, therefore no further factorization is possible

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

416, 1000

are

= 2 \cdot 2 \cdot 2

Multiply the numbers:

2 \cdot 2 \cdot 2 = 8

= 8

Factor out

8

from the numerator and the denominator

416 = 8 \cdot 52, 1000 = 8 \cdot 125

= \frac{8 \cdot 52}{8 \cdot 125}

Cancel the common factor:

8

= \frac{52}{125}

= \frac{52}{125}

Popular Examples

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\frac{45}{10}

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t o a p erce n t a g e 75/20

Convert to a Mixed Number 52/5 mixed number

\frac{52}{5}

Frequently Asked Questions (FAQ)

What is dectofrac 0.416 ?
The solution to dectofrac 0.416 is 52/125