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Answer :
To convert the mixed number [tex]\(69 \frac{7}{9}\)[/tex] to a decimal, follow these steps:
1. Break down the mixed number: The mixed number [tex]\(69 \frac{7}{9}\)[/tex] consists of a whole number part (69) and a fractional part ([tex]\(\frac{7}{9}\)[/tex]).
2. Convert the fractional part to a decimal: The fraction [tex]\(\frac{7}{9}\)[/tex] can be converted to a decimal by dividing 7 by 9.
[tex]\[
7 \div 9 = 0.7777\ldots
\][/tex]
This is a repeating decimal and can be represented as [tex]\(0.\overline{7}\)[/tex], where the bar over the 7 indicates that it repeats indefinitely.
3. Combine the whole number and the decimal: Add the whole number part (69) to the decimal part [tex]\(0.\overline{7}\)[/tex].
[tex]\[
69 + 0.\overline{7} = 69.\overline{7}
\][/tex]
So, [tex]\(69 \frac{7}{9}\)[/tex] as a decimal is [tex]\(69.\overline{7}\)[/tex].
The correct option from the choices provided is:
[tex]$69 . \overline{7}$[/tex]
1. Break down the mixed number: The mixed number [tex]\(69 \frac{7}{9}\)[/tex] consists of a whole number part (69) and a fractional part ([tex]\(\frac{7}{9}\)[/tex]).
2. Convert the fractional part to a decimal: The fraction [tex]\(\frac{7}{9}\)[/tex] can be converted to a decimal by dividing 7 by 9.
[tex]\[
7 \div 9 = 0.7777\ldots
\][/tex]
This is a repeating decimal and can be represented as [tex]\(0.\overline{7}\)[/tex], where the bar over the 7 indicates that it repeats indefinitely.
3. Combine the whole number and the decimal: Add the whole number part (69) to the decimal part [tex]\(0.\overline{7}\)[/tex].
[tex]\[
69 + 0.\overline{7} = 69.\overline{7}
\][/tex]
So, [tex]\(69 \frac{7}{9}\)[/tex] as a decimal is [tex]\(69.\overline{7}\)[/tex].
The correct option from the choices provided is:
[tex]$69 . \overline{7}$[/tex]
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