Answer:
[tex]\frac{8}{9}[/tex]
Step-by-step explanation:
Given
Series: 0.8 + 0.08 + 0.008 + 0.0008 + ...
Required
Determine a rational number to represent the series
To do this, we simply get the sum to infinity of the series;
This is done as follows;
[tex]S = \frac{a}{1 - r}[/tex]
Where a represent the first term
[tex]a = 0.8[/tex]
r represent the common ratio
[tex]r = \frac{0.08}{0.8}[/tex]
[tex]r = 0.1[/tex]
Substitute these values in the above formula
[tex]S = \frac{0.8}{1 - 0.1}[/tex]
[tex]S = \frac{0.8}{0.9}[/tex]
Multiply the numerator and denominator by 10
[tex]S = \frac{8}{9}[/tex]
Hence;
The number is [tex]\frac{8}{9}[/tex]
