Show me how to change this decimal to a fraction. 0.98 (both the 9 and 8 repeat) Can someone show me the work for this question

Question

Show me how to change this decimal to a fraction.
0.98 (both the 9 and 8 repeat)
Can someone show me the work for this question

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Thiên Thanh 1 week 2021-07-19T16:38:51+00:00 1 Answers 1 views 0

Answers ( )

    0
    2021-07-19T16:40:30+00:00

    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}}

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