Question

How do we convert $2.16$ ( $6$ repeating ) to a fraction?

Answer 1

Hint: Decimal number can be defined as a number whose whole number part and the fractional part is separated by a decimal point. Here note that $0.16666...$ is equivalent to ${\displaystyle \frac{1}{6}}$ .

Complete step by step answer:
We can use the sum of fractions to write out the decimal:
For this particular question , We can see that $0.16666...$ is the fraction ${\displaystyle \frac{1}{6}}$,

Therefore the given decimal $2.16666....$=$2+{\displaystyle \frac{1}{6}}={\displaystyle \frac{13}{6}}$.

Note: $2.16$ is a repeating decimal number and we want to convert it to a fraction or mixed number When we say $2.16$ repeating, we could mean that $6$ or $16$ is repeating.
Thus, there are two different ways of answering “ What is $2.16$ repeating as a fraction? “ Here are the two questions formulated in mathematical terms with the vinculum line above the decimal numbers that are repeating. $2.1\bar{6}$ repeating as a fraction. $2.1\bar{6}$ repeating as a fraction.
The formula to convert any repeating decimal number to a fraction is as follows:
${\displaystyle \frac{(DN\times F)-NRP}{D}}$
DN= Decimal Number
F= if one repeating number, if two repeating numbers, if three repeating numbers, etc.
NRP=Non –repeating part of a decimal number.
D= If one repeating numbers, if two repeating numbers, if three repeating numbers, etc.
Convert the decimal number to a fraction by placing the decimal number over the power of ten. Since there are numbers to the right of the decimal point, place the decimal number over.