Answer:
0.26 repeating as a fraction is [tex]\frac{4}{15}[/tex]
Step-by-step explanation:
Given : Expression 0.26 repeating.
To find : What is expression as a fraction?
Solution :
Let [tex]x=0.26666[/tex] ....(1)
Multiply both side by 10,
[tex]10x=2.666...[/tex] .....(2)
Subtract (1) and (2),
[tex]10x-x=(2.666...)-(0.2666...)[/tex]
[tex]9x=2.4[/tex]
[tex]x=\frac{2.4}{9}[/tex]
[tex]x=\frac{24}{90}[/tex]
[tex]x=\frac{4}{15}[/tex]
Therefore, 0.26 repeating as a fraction is [tex]\frac{4}{15}[/tex]
