Question

4. Which of these non-terminating decimals can be converted into a rational number? A. 0.874387438743... B. 0.0000100020003... C. 5.891420975 D. 10.07401259...

Answer 1

Answer: A. 0.874387438743.. is  a rational number.

Step-by-step explanation:

Since Any number that can be written in fraction form is a rational number if it can be in the form of p/q where p and q are integers and q≠0

Since we can write 0.874387438743... = $\frac{8743}{9999}$

Where, 8743 and 9999 are integers and 9999≠0

Thus, 0.874387438743... is a rational number.

But, 0.0000100020003... ,  5.891420975..... and 10.07401259... can not be written in the form of p/q therefore they are not the rational number.

Therefore, Only Option A is correct.