Recurring (Problem 1 1 )

Number Theory Level 2

True or False?

0. 9 ‾ 8 = 1 ? \quad 0.\overline{9}8 = 1?

True False This is an impossible scenario

Yajat Shamji by Yajat Shamji , 16, United Kingdom

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1 solution

Yajat Shamji
Jun 30, 2020

x = 0. 9 ‾ 8 x = 0.\overline{9}8

10 x = 9. 9 ‾ 8 10x = 9.\overline{9}8

10 x − x = 9 x 10x - x = 9x

9. 9 ‾ 8 − 0. 9 ‾ 8 = 9 9.\overline{9}8 - 0.\overline{9}8 = 9

9 x = 9 9x = 9

9 x 9 \frac{9x}{9} = 9 9 \frac{9}{9}

x = 1 x = 1

Answer = True \fbox{\text{True}}

0 Helpful 0 Interesting 0 Brilliant 3 Confused

How exactly there be a number with infinite plus one decimal digits?

Nazzarena Labò - 11 months, 2 weeks ago

I selected true, why am I wrong @Yajat Shamji ?

Frisk Dreemurr - 11 months, 2 weeks ago

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The staff has changed the answer.

Yajat Shamji - 11 months, 2 weeks ago

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