Question

Which of the following numbers can be expressed as repeating decimals? (5 points)

3 over 7 , 2 over 5 , 3 over 4 , 2 over 9 How can 38 over 6 be expressed as a decimal?

Answer 1

9514 1404 393

Answer:

Repeating decimals:

• 3/7
• 2/9

38/6 = 6.3_3 (repeating 3)

Explanation:

`(3)/(7)=0.\overline{428571} \quad\text{repea}\text{ting decimal}\\\\(2)/(5)=0.4\\\\(3)/(4)=0.75\\\\(2)/(9)=0.\overline{2}\quad\text{repea}\text{ting decimal}`

The improper fraction 38/6 = 19/3 = 6 1/3. As a decimal, this is ...

`(19)/(3)=6.\overline{3}\quad\text{repea}\text{ting decimal}`

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The repeating part of a decimal fraction is conventionally written with an overbar, as shown in the typeset content above. In plain text, it is sometimes written with an underscore preceding the repeating digits.