Question

Whats 2.16 as a fraction?

Answer 1

If we have a decimal number and we want to convert it to a fraction, we can start by multiplying (and also dividing) by 10^n, being n the number of decimals of the number.

In this case, 2.16 has 2 decimal places, so we have to multiply and divide it by 10^2=100.

Then, we get:

`2.16\cdot(100)/(100)=(2.16\cdot100)/(100)=(216)/(100)`

We already have a fraction: 216/100, but we can try to simplify if looking for common factors:

`\begin{gathered} 216=2\cdot108=2\cdot2\cdot54=2\cdot2\cdot2\cdot27=2^3\cdot3\cdot9=2^3\cdot3\cdot3\cdot3=2^3\cdot3^3 \\ 100=2^2\cdot25=2^2\cdot5^2 \end{gathered}`

We have 2^2=4 as common factor between numerator and denominator, so we can simplify the fraction as:

`((216)/(4))/((100)/(4))=(54)/(25)`

Answer: 2.16 as a fraction is 54/25.