3.7 repeating as a mixed number

Answer: Our required mixed number is [tex]3\dfrac{7}{9}[/tex]Step-by-step explanation:Since we have given that [tex]x=3.\bar{7}[/tex]We need to rewrite it in a mixed number.Since x = 3.7777777..........--------(1)Multiplying by 10 on both the sides, we get that 10x=37.777777.............-------------(2)Now, subtract (2) - (1), we get that [tex]10x-x=37.7777-3.7777\\\\9x=34\\\\x=\dfrac{34}{9}[/tex]So, we need to write in mixed number that is given by[tex]\dfrac{34}{9}=3\dfrac{7}{9}[/tex]Hence, our required mixed number is [tex]3\dfrac{7}{9}[/tex]