What is dectofrac 3.375 ?

The solution to dectofrac 3.375 is 3 3/8

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Popular >

Convert to a Simplified Fraction 3.375

Solution

decimal to fraction

3.375

Solution

3 \frac{3}{8}

Solution steps

3.375

Rewrite as

= 3 + 0.375

Convert

0.375

to a fraction:

\frac{3}{8}

0.375

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{0.375 \cdot 1000}{1000}

= \frac{375}{1000}

Reduce the fraction

\frac{375}{1000} : \frac{3}{8}

\frac{375}{1000}

Find a common factor of

375

and

1000

in order to cancel it out

Greatest Common Divisor of

375, 1000 : 125

375, 1000

Greatest Common Divisor (GCD)

Prime factorization of

375 : 3 \cdot 5 \cdot 5 \cdot 5

375

375

divides by

3375 = 125 \cdot 3

= 3 \cdot 125

125

divides by

5125 = 25 \cdot 5

= 3 \cdot 5 \cdot 25

25

divides by

525 = 5 \cdot 5

= 3 \cdot 5 \cdot 5 \cdot 5

3, 5

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 5 \cdot 5 \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

375, 1000

are

= 5 \cdot 5 \cdot 5

Multiply the numbers:

5 \cdot 5 \cdot 5 = 125

= 125

Factor out

125

from the numerator and the denominator

375 = 125 \cdot 3, 1000 = 125 \cdot 8

= \frac{125 \cdot 3}{125 \cdot 8}

Cancel the common factor:

125

= \frac{3}{8}

= \frac{3}{8}

= 3 + \frac{3}{8}

= 3 \frac{3}{8}

Popular Examples

180/7 long division

\frac{180}{7}

Convert to an Improper Fraction 3 3/5 improper fraction

3 \frac{3}{5}

81-64 long subtraction

81 - 64

50/20 long division

\frac{50}{20}

1500/3 long division

\frac{1500}{3}

Frequently Asked Questions (FAQ)

What is dectofrac 3.375 ?
The solution to dectofrac 3.375 is 3 3/8