Respuesta :
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:
[tex]2.16\cdot\frac{100}{100}=\frac{2.16\cdot100}{100}=\frac{216}{100}[/tex]We already have a fraction: 216/100, but we can try to simplify if looking for common factors:
[tex]\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}[/tex]We have 2^2=4 as common factor between numerator and denominator, so we can simplify the fraction as:
[tex]\frac{\frac{216}{4}}{\frac{100}{4}}=\frac{54}{25}[/tex]Answer: 2.16 as a fraction is 54/25.
