Question

Write as a fraction or mixed number and write in simplest form 3.6416=

Answer 1

Decimal to fraction conversion

We are given the decimal number N=3.6416

Any number with a limited number of decimals can be converted to a fraction by multiplying and dividing by a power of 10, in this case:

`N=3.6416=(3.6416\cdot10000)/(10000)=(36416)/(10000)`

The selection of the power of 10 is such that the numerator does not have a decimal expression anymore.

Now we have an equivalent fraction, we must simplify it in its simplest form.

Both the numerator and the denominator are even numbers, so we simplify by dividing by 2 as many times as possible:

`N=(36416)/(10000)=(18298)/(5000)=(9104)/(2500)=(4552)/(1250)=(2276)/(625)`

The denominator is only divisible by 5 and the numerator is not, thus the simplest fraction is:

`N=(2276)/(625)`

To express it as a mixed number, we subtract 3*625= 1875 to the numerator as follows:

`N=(1875+401)/(625)=(1875)/(625)+(401)/(625)=3+(401)/(625)=3(401)/(625)`

The answer is:

`N=3(401)/(625)`