Express 0.1 6 (that is, 0.1666…) as a fraction in lowest terms.

1/6. x = 0.1666… → 10x = 1.666…, 100x = 16.666… Subtract: 90x = 15 → x = 15/90 = 1/6. 16/99 treats 16 as the repeating block.

Express $0.1 \overline{6}$ (that is, 0.1666…) as a fraction in lowest terms.

Class 8Rational Numbers as DecimalsRational Numbers

x = 0.1666

… →

10 x = 1.666

…,

100 x = 16.666

… Subtract:

90 x = 15

→

x = \frac{15}{90} = \frac{1}{6} . \frac{16}{99}

treats 16 as the repeating block.

Answer: B)

\frac{1}{6}

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