Answer:
x = [tex]\frac{7}{15}[/tex].
Step-by-step explanation:
Given : 0.46 with 6 repeating .
To find : repeating as a fraction
Given : We have given 0.46666
Let x = 0.4666...
By the recurring rule .
On multiplying both sides by 10
10 x = 10 * 0.466666
10x = 4.66666
we can write 4.666 in term of x
4.2 + 0.46666
10x = 4.2 + 0.46666
10x = 4.2 + x .
10x -x = 4.2
9x = 4.2
On dividing both sides by 9
x = [tex]\frac{4.2}{9}[/tex].
x = [tex]\frac{42}{90}[/tex].
x = [tex]\frac{7}{15}[/tex].
Therefore, x = [tex]\frac{7}{15}[/tex].
