Write 3.7 as a mixed number.

Let [tex] x = 3.7 [/tex]

[tex] 10x = 37 [/tex]

[tex] 9x = 33.3\overline{3} [/tex]

[tex] x = 3.\overline{7} [/tex]

So, [tex] 3.\overline{7} [/tex] is equal to [tex] 3 \frac{7}{10} [/tex]



Answer :

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

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

2. Multiply by 10 to shift the repeating decimal:
[tex]\[ 10x = 37.\overline{7} \][/tex]

3. Subtract the original [tex]\( x \)[/tex] from this value:
[tex]\[ 10x - x = 37.\overline{7} - 3.\overline{7} \][/tex]
[tex]\[ 9x = 34 \][/tex]

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

5. Convert the improper fraction to a mixed number. Divide 34 by 9:
[tex]\[ 34 \div 9 = 3 \text{ remainder } 7 \][/tex]
This results in the mixed number:
[tex]\[ 3 \frac{7}{9} \][/tex]

So, [tex]\(3.\overline{7}\)[/tex] is equal to:
[tex]\[ 3 \frac{7}{9} \][/tex]