Which of the following rational numbers can be expressed as a repeating decimal: 7/8, 5/12, 17/25, or 31/40?(1 point)
The rational numbers that can be expressed as a repeating decimal are the ones with denominators that are not divisible only by 2 or 5.
Out of the given options, only 7/8, 5/12, and 31/40 have denominators that are not divisible only by 2 or 5.
7/8 = 0.875 (terminating decimal)
5/12 = 0.416666... (repeating decimal)
17/25 = 0.68 (terminating decimal)
31/40 = 0.775 (terminating decimal)
Therefore, the rational numbers that can be expressed as a repeating decimal are 5/12. (B)
Express 713 as a repeating decimal. Mark the repeating digits with a bar.
Note: You will find the option to add a bar above text in the Geometry (∠) keyboard.
(1 point)
To determine which of the given rational numbers can be expressed as a repeating decimal, we need to check if the denominator has any prime factors other than 2 and 5.
Let's examine each rational number:
1. 7/8: The denominator is 8, which can be factored as 2 x 2 x 2. Since there are no prime factors other than 2 and 5, the decimal representation of 7/8 will terminate, not repeat.
2. 5/12: The denominator is 12, which can be factored as 2 x 2 x 3. Again, there are no prime factors other than 2 and 5, so the decimal representation of 5/12 will also terminate, not repeat.
3. 17/25: The denominator is 25, which is already a perfect square. Since there are no prime factors other than 2 and 5, the decimal representation of 17/25 will terminate, not repeat.
4. 31/40: The denominator is 40, which can be factored as 2 x 2 x 2 x 5. Since 2 is the only prime factor other than 2 and 5, the decimal representation of 31/40 will repeat.
Therefore, the rational number 31/40 can be expressed as a repeating decimal.
To determine which of the given rational numbers can be expressed as a repeating decimal, we need to examine their decimal representations. We can do this by performing the division operation.
Let's start with 7/8:
When we divide 7 by 8, we get 0.875, which terminates and does not repeat. So, 7/8 cannot be expressed as a repeating decimal.
Next, let's take 5/12:
When we divide 5 by 12, we get 0.416666..., which has a repeating decimal pattern of 6. So, 5/12 can be expressed as a repeating decimal.
Moving on to 17/25:
When we divide 17 by 25, we get 0.68, which terminates and does not repeat. Therefore, 17/25 cannot be expressed as a repeating decimal.
Lastly, let's consider 31/40:
When we divide 31 by 40, we get 0.775, which also terminates and does not repeat. Hence, 31/40 cannot be expressed as a repeating decimal.
Therefore, the rational number that can be expressed as a repeating decimal is 5/12.