Part I: Defining "Repeating decimals"
Repeating decimals refers to a specific number being repeated after the decimal point in a decimal. Repeating decimals never terminates.
A few examples of repeating decimals can be 8.8888... or 8.818181...
Part II: Verifying all options and choosing the correct choice
Now, let's convert the fractions into decimals using a calculator:
- A) 3/7 ⇔ 0.428571428571...
- D) 2/9 ⇔ 0.22222222222...
Option A
This option is classified as a repeating decimal because there is specific number being repeated after the decimal point in 3/7 (428571).
To avoid confusion, we can split the decimal shown below.
⇒ A) 3/7 ⇒ [tex]0.428571428571...[/tex] ⇒ [tex]0.\underline{428571} \ \underline{428571}...[/tex]
It also has the three dots, which indicates that the number does not terminate. Therefore, 3/7 a repeating decimal.
Option B
This option is a terminating decimal. Terminating decimals are not allowed in repeating decimals. Therefore, 2/5 is not a repeating decimal
Option C
This option is a terminating decimal. Terminating decimals are not allowed in repeating decimals. Therefore, 3/4 is not a repeating decimal.
Option D
We can see that 2/9 has a specific number being repeated after the decimal point, which is 2. It also has the three dots, which indicates that the number does not terminate. Therefore, 2/9 is a repeating decimal
