Which number(s) below represents a repeating decimal?
1/3,- 3/8, 7/10, 14/20
enter the fractions into your calculator
numerator (top) divided by denominator (bottom)
To determine if a number represents a repeating decimal, we need to find if its fraction form has a denominator that is not a power of 10. Let's analyze each given number:
1. 1/3: When we divide 1 by 3, it results in a decimal of 0.333... The number 1/3 represents a repeating decimal.
2. -3/8: When we divide -3 by 8, it results in a decimal of -0.375. The number -3/8 does not represent a repeating decimal.
3. 7/10: When we divide 7 by 10, it results in a decimal of 0.7. The number 7/10 does not represent a repeating decimal.
4. 14/20: When we divide 14 by 20, it results in a decimal of 0.7. The number 14/20 does not represent a repeating decimal.
So, out of the given numbers, only 1/3 represents a repeating decimal.
To determine if a number represents a repeating decimal, you need to check if it can be expressed as a fraction where the denominator is **not** a power of 10, such as 10, 100, 1000, and so on. In other words, fractions that can't be simplified to have a denominator in the form of 10^n, where "n" is a positive integer.
Let's check the numbers you provided:
1/3 is a repeating decimal because 3 is not a power of 10.
-3/8 is NOT a repeating decimal because 8 can be simplified to have a denominator of 10. We can multiply the fraction by 5/5 to get -15/40, which simplifies to -3/8.
7/10 is NOT a repeating decimal because 10 can be simplified to have a denominator of 10. It is already in simplified form.
14/20 is NOT a repeating decimal because 20 can be simplified to have a denominator of 10. We can divide both the numerator and denominator by 2 to get 7/10.
Therefore, the only number that represents a repeating decimal among the given options is 1/3.