Question

match each rational number in the first column with an equal rational number in the second column.
1 ( 0.overline{17} ) 2 ( 0.overline{017} ) 3 ( 0.125 ) 4 ( \frac{3}{8} ) 5 ( \frac{4}{15} ) 6 ( 0.28 ) 7 ( \frac{2}{5} ) 8 ( 0.04 )
match each of the options above to the items below.
( \frac{7}{25} )
( \frac{17}{99} )
( 0.375 )
( \frac{1}{25} )
( \frac{5}{27} )
( \frac{617}{999} )
( 0.2overline{6} )
( 0.overline{4} )

Explanation:

Step1: Convert $\frac{1}{25}$ to decimal

$\frac{1}{25} = 1 \div 25 = 0.04$

Step2: Convert $\frac{17}{99}$ to decimal

$\frac{17}{99} = 17 \div 99 = 0.\overline{17}$

Step3: Convert 0.375 to fraction

$0.375 = \frac{375}{1000} = \frac{3}{8}$

Step4: Convert $\frac{1}{8}$ to decimal

$\frac{1}{8} = 1 \div 8 = 0.125$

Step5: Convert $\frac{7}{25}$ to decimal

$\frac{7}{25} = 7 \div 25 = 0.28$

Step6: Convert $\frac{17}{999}$ to decimal

$\frac{17}{999} = 17 \div 999 = 0.\overline{017}$

Step7: Convert $0.\overline{26}$ to fraction

Let $x=0.\overline{26}=0.262626...$, $100x=26.262626...$
$100x - x = 26$, so $x=\frac{26}{99}=\frac{2}{7.615}$ corrected: $100x-x=26 \implies 99x=26 \implies x=\frac{26}{99}$ no, wait $\frac{4}{15}=0.2666...$ corrected: $0.\overline{26}$ is $\frac{26}{99}$, but $\frac{4}{15}=0.2\overline{6}$. Wait, $\frac{4}{15}=4\div15=0.2666...=0.2\overline{6}$

Step8: Convert $0.\overline{6}$ to fraction

Let $x=0.\overline{6}=0.666...$, $10x=6.666...$
$10x - x = 6$, so $x=\frac{6}{9}=\frac{2}{3}$

Answer:

• $\frac{1}{25}$: 8. 0.04
• $\frac{17}{99}$: 1. $0.\overline{17}$
• 0.375: 4. $\frac{3}{8}$
• $\frac{1}{8}$: 3. 0.125
• $\frac{7}{25}$: 6. 0.28
• $\frac{17}{999}$: 2. $0.\overline{017}$
• $0.2\overline{6}$: 5. $\frac{4}{15}$
• $0.\overline{6}$: 7. $\frac{2}{3}$