You are given a fraction in simplest form. The numerator is not zero. When you write the fraction as a decimal, it is a repeating decimal. Which numbers from 1 to 10 could be the denominator?

THANK YOU!

1/3 7/3 and 5/3 end in recurring digits but three is not the only one because 1/6 and 5/6 and 7/6 give recurring as well and 1, 5 and 7 / 9. I believe 7 may be aswell but my calculator doesn't go far enough for me to see a pattern.

So overall 3, 6, 9 and I believe 7

yes, a denominator of 7 results in a repeating decimal.

e.g. 4/7 = .571428571..
with the repeat as 571428

interesting to note:
1/7 = .142857142...
2/7 = .285714285..
etc
notice the repeat sequence is the same, it just starts at a different digit
try it with the other proper fractions of 7

To determine which numbers from 1 to 10 could be the denominator of a fraction that, when written as a decimal, is a repeating decimal, we can use the following approach:

Step 1: Convert the fraction to a decimal.
Step 2: Check if the decimal representation of the fraction repeats.

Let's go through each number from 1 to 10 as potential denominators and find out if they meet the given conditions.

1. Denominator = 1:
Any fraction with a denominator of 1 will have a decimal representation without any fractional part. Therefore, it will not be a repeating decimal.

2. Denominator = 2:
If the numerator is odd, the fraction will not represent a repeating decimal when divided. For example, 1/2 = 0.5, which does not repeat.

3. Denominator = 3:
For a fraction with a denominator of 3, if the numerator is divisible evenly by 3, the decimal representation will repeat. For example, 2/3 = 0.666..., where 6 repeats.

4. Denominator = 4:
A fraction with a denominator of 4 will not represent a repeating decimal. For example, 1/4 = 0.25, which does not repeat.

5. Denominator = 5:
Any fraction with a denominator of 5 that does not have a numerator divisible by 5 will not represent a repeating decimal. For example, 1/5 = 0.2, which does not repeat.

6. Denominator = 6:
A fraction with a denominator of 6 will not represent a repeating decimal. For example, 1/6 = 0.1666..., which does not repeat.

7. Denominator = 7:
When the numerator is not divisible by 7, the fraction will represent a repeating decimal. For example, 3/7 = 0.428571..., where 428571 repeats.

8. Denominator = 8:
A fraction with a denominator of 8 will not represent a repeating decimal. For example, 1/8 = 0.125, which does not repeat.

9. Denominator = 9:
When the numerator is not divisible by 9, the fraction will represent a repeating decimal. For example, 2/9 = 0.222..., where 2 repeats.

10. Denominator = 10:
Any fraction with a denominator of 10 will have a decimal representation without any repeating digits. For example, 1/10 = 0.1, which does not repeat.

Based on this analysis, the numbers from 1 to 10 that could be the denominator of a fraction where the decimal representation is repeating are: 3, 7, and 9.