What is tofraction 2.16 ?

The solution to tofraction 2.16 is 2 4/25

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Popular Pre Algebra >

Convert to a Simplified Fraction 2.16

Solution

convert to fraction

2.16

Solution

2 \frac{4}{25}

Decimal

2.16

Solution steps

2.16

Rewrite as

= 2 + 0.16

Convert

0.16

to a fraction:

\frac{4}{25}

0.16

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

There are

2

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

100

= \frac{0.16 \cdot 100}{100}

= \frac{16}{100}

Reduce the fraction

\frac{16}{100} : \frac{4}{25}

\frac{16}{100}

Find a common factor of

16

and

100

in order to cancel it out

Greatest Common Divisor of

16, 100 : 4

16, 100

Greatest Common Divisor (GCD)

Prime factorization of

16 : 2 \cdot 2 \cdot 2 \cdot 2

16

16

divides by

216 = 8 \cdot 2

= 2 \cdot 8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2

Prime factorization of

100 : 2 \cdot 2 \cdot 5 \cdot 5

100

100

divides by

2100 = 50 \cdot 2

= 2 \cdot 50

50

divides by

250 = 25 \cdot 2

= 2 \cdot 2 \cdot 25

25

divides by

525 = 5 \cdot 5

= 2 \cdot 2 \cdot 5 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 5 \cdot 5

The prime factors common to

16, 100

are

= 2 \cdot 2

Multiply the numbers:

2 \cdot 2 = 4

= 4

Factor out

4

from the numerator and the denominator

16 = 4 \cdot 4, 100 = 4 \cdot 25

= \frac{4 \cdot 4}{4 \cdot 25}

Cancel the common factor:

4

= \frac{4}{25}

= \frac{4}{25}

= 2 + \frac{4}{25}

= 2 \frac{4}{25}

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Frequently Asked Questions (FAQ)

What is tofraction 2.16 ?
The solution to tofraction 2.16 is 2 4/25

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