Question

How many repeating digits in 0.64?0123What value is multiplied on both sides of the equation sign?0101001000What fraction represents 0.64?64/999964/99964/9964/9

Answer 1

Since the line is over the numbers 6 and 4, then there are 2 repeating digits, that is:

`0.\bar{64}=0.64646464\ldots`

Now, create an equation such that x equals the decimal number:

`\begin{gathered} x=0.\bar{64} \\ x=0.6464\ldots\Rightarrow\text{ Equation 1} \end{gathered}`

Since 2 figures are repeated then multiply by 100 on both sides of the equation:

`\begin{gathered} 100\cdot x=0.\bar{64}\cdot100 \\ 100x=64.6464\ldots\Rightarrow\text{ Equation 2} \end{gathered}`

Now subtract equation 1 from equation 2:

`\begin{gathered} 100x=64.6464 \\ x=0.6464\text{ -} \\ ---------- \\ 99x=64 \end{gathered}`

Finally, solve for x

`\begin{gathered} 99x=64 \\ \text{ Divide by 99 into both sides of the equation} \\ (99x)/(99)=(64)/(99) \\ x=(64)/(99) \end{gathered}`

Therefore, the fraction that represents 0.64 is

`(64)/(99)`