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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

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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1 vote
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

User Ekkis
by
8.0k points

1 Answer

4 votes

Answer:

98/99

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 = (98)/(99) \\ \implies \huge \red{0.\overline{98}} = \orange{(98)/(99)}

User Kaoutar
by
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