8. Write 3.7 as a mixed number.

Let [tex]\( x = \square \)[/tex]

[tex]\[ 10x = \square \][/tex]

[tex]\[ 9x = \square \][/tex]

[tex]\[ x = \square \][/tex]

So, [tex]\( 3.\overline{7} \)[/tex] is equal to [tex]\(\square\)[/tex].



Answer :

To write [tex]\(3.\overline{7}\)[/tex] (3.7777...) as a mixed number, follow these steps:

1. Let [tex]\( x = 3.\overline{7} \)[/tex]:
[tex]\[ x = 3.777777\ldots \][/tex]

2. Multiply [tex]\( x \)[/tex] by 10:
[tex]\[ 10x = 37.777777\ldots \][/tex]

3. Subtract [tex]\( x \)[/tex] from [tex]\( 10x \)[/tex]:
[tex]\[ 10x - x = 37.777777\ldots - 3.777777\ldots \][/tex]
[tex]\[ 9x = 34 \][/tex]

4. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{34}{9} \][/tex]

So, the mixed number representation of [tex]\(3.\overline{7}\)[/tex] is:

[tex]\[ 3.\overline{7} = \frac{34}{9} \][/tex]