Question

Show me how to change this decimal to a fraction.

Answer 1

Answer:

98/99

Step-by-step explanation:

0.98 (both the 9 and 8 repeat)

$0.98 (both \: the \: 9 \: and \: 8 \: repeat) = 0.\overline{98} \\ let \: x = 0.\overline{98}...(1) \\ multiply \: both \: side \: of \: eq \: (1) \: by \: 100 \\ 100x = 98.\overline{98}...(2) \\ equation \: (2) - equation \: (1) \\ 100x - x = 98.\overline{98} - 0.\overline{98} \\ 99x = 98 \\ x = \frac{98}{99} \\ \implies \huge \red{0.\overline{98}} = \orange{\frac{98}{99}}$