Which of these nonterminating decimals can be converted into a rational number?

A 0.48907542 repeating
B 0.02020202 repeating
C 0.92589542 repeating
D 0.10203040 repeating

My answer is B
Am I correct?
If not PLZ help me

it looks correct

any repeating decimal can be converted to a rational number

all of the responses are labeled "repeating" ... confusing

Okay, thank you so much

Hope you have a great day !!

To determine which of the nonterminating decimals can be converted into rational numbers, we need to check if they can be expressed as a fraction of two integers (p/q) where q is not equal to zero.

Let's examine each option:

A) 0.48907542 repeating:
To determine if this can be expressed as a rational number, we can rewrite it as an equation:

x = 0.48907542...
10x = 4.8907542...
Subtracting the equation x = 0.48907542... from 10x = 4.8907542..., we get:

9x = 4.4016798...
Simplifying, we have:

x = 4.4016798... / 9

Since the numerator (4.4016798...) is not an integer, A cannot be expressed as a rational number.

B) 0.02020202 repeating:
We can rewrite this decimal as an equation in the same way as above:

x = 0.020202...
100x = 2.020202...
Subtracting x = 0.020202... from 100x = 2.020202..., we get:

99x = 2
x = 2/99

Since both the numerator and denominator are integers, B can be expressed as a rational number.

C) 0.92589542 repeating:
Again, we can rewrite this as an equation:

x = 0.92589542...
100x = 92.589542...
Subtracting x = 0.92589542... from 100x = 92.589542..., we get:

99x = 91.66364758...
x = 91.66364758... / 99

Since the numerator (91.66364758...) is not an integer, C cannot be expressed as a rational number.

D) 0.10203040 repeating:
Let's rewrite this decimal as an equation:

x = 0.10203040...
1000x = 102.03040...
Subtracting x = 0.10203040... from 1000x = 102.03040..., we get:

999x = 101.9283696...
x = 101.9283696... / 999

Since the numerator (101.9283696...) is not an integer, D cannot be expressed as a rational number.

Based on this analysis, you are correct that option B (0.02020202 repeating) can be converted into a rational number.

I hope this helps! Let me know if you have any further questions.