Can someone check this?
11. Which of these nonterminating decimals can be converted into a rational number?
***a. 0.626226222...
b. 0.020220222...
c. 0.123123123...
d. 0.898998999...
Thanks for the help,
Luna
Then the answer is c?
To determine if a nonterminating decimal can be converted into a rational number, we need to check if the decimal repeats itself in a pattern. A rational number is any decimal that can be written as a fraction in the form a/b, where a and b are integers.
Looking at the options provided:
a. 0.626226222...
The decimals 6, 2, and 2 repeat themselves in a pattern: 626. Therefore, this decimal can be converted into a rational number.
b. 0.020220222...
The decimals do not repeat in a pattern. Since there is no repeating pattern, this decimal cannot be converted into a rational number.
c. 0.123123123...
The decimals 1, 2, and 3 repeat themselves in a pattern: 123. Therefore, this decimal can be converted into a rational number.
d. 0.898998999...
The decimals 8 and 9 repeat themselves in a pattern: 89. Therefore, this decimal can be converted into a rational number.
Based on the repeating patterns in the options, the nonterminating decimals that can be converted into rational numbers are:
a. 0.626226222...
c. 0.123123123...
d. 0.898998999...
Hope this helps! Let me know if you have any more questions.
nope. only repeating decimals are rational.
(a) does not repeat the same digit group over and over.