Determine if these fractions are repeating or terminating as a decimal. 3/8 2/3 5/6 13/8
To determine if a fraction is repeating or terminating as a decimal, we need to examine the denominator (the bottom number).
3/8: This fraction is terminating because the denominator, 8, is a power of 2, and dividing by powers of 2 always results in a finite decimal.
2/3: This fraction is repeating because the denominator, 3, is not a power of 2, and dividing by 3 will result in a repeating decimal.
5/6: This fraction is repeating because the denominator, 6, is not a power of 2, and dividing by 6 will result in a repeating decimal.
13/8: This fraction is terminating because the denominator, 8, is a power of 2, and dividing by powers of 2 always results in a finite decimal.
In summary:
3/8 is terminating.
2/3 and 5/6 are repeating.
13/8 is terminating.
To determine if these fractions are repeating or terminating as decimals, we need to perform the division.
1. Let's start with 3/8:
- Divide 3 by 8: 3 ÷ 8 = 0.375
- The decimal terminates after three decimal places, so 3/8 is terminating.
2. Moving on to 2/3:
- Divide 2 by 3: 2 ÷ 3 = 0.666...
- The decimal starts repeating after two decimal places, indicating that 2/3 is repeating.
3. Next, let's consider 5/6:
- Divide 5 by 6: 5 ÷ 6 = 0.833...
- The decimal starts repeating after three decimal places, indicating that 5/6 is repeating.
4. Lastly, let's examine 13/8:
- Divide 13 by 8: 13 ÷ 8 = 1.625
- The decimal terminates after three decimal places, so 13/8 is terminating.
To summarize:
- 3/8 is terminating.
- 2/3 and 5/6 are repeating.
- 13/8 is terminating.