4.5 Recurring decimals — Practise

1. Answer 1

Answer: $x=0.333\ldots$, so $10x=3.333\ldots$. Subtract: $9x=3$, hence $x=\frac{1}{3}.$

2. Answer 2

Answer: $0.272727\ldots=\frac{27}{99}=\frac{3}{11}.$

3. Answer 3

Answer: $x=0.1666\ldots$. Then $10x=1.666\ldots$ and $100x=16.666\ldots$; subtract to get $90x=15$, so $x=\frac{1}{6}.$

4. Answer 4

Answer: $0.\dot{5}=\frac{5}{9}$ and $0.\dot{2}=\frac{2}{9}$, so the sum is $\frac{7}{9}.$

5. Answer 5

Answer: $0.\dot{4}=\frac{44}{99}>\frac{43}{99}=0.\dot{4}\dot{3}$.