Rational Numbers in Different Forms Practice
Math 8 Q1 (Pre-Algebra) / The Number System
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 5/12 and 31/40.
To determine which of the given rational numbers can be expressed as a repeating decimal, we need to convert each fraction into decimal form.
Let's start with 7/8:
To convert 7/8 into a decimal, we can divide the numerator (7) by the denominator (8):
7 ÷ 8 = 0.875
Since the division terminates and does not repeat, 7/8 can be expressed as a terminating decimal.
Next, let's convert 5/12 into a decimal:
5 ÷ 12 = 0.416666...
The division continues infinitely, with the digit 6 repeating in the decimal. Therefore, 5/12 can be expressed as a repeating decimal.
Now, let's convert 17/25 into a decimal:
17 ÷ 25 = 0.68
Since the division terminates and does not repeat, 17/25 can be expressed as a terminating decimal.
Finally, let's convert 31/40 into a decimal:
31 ÷ 40 = 0.775
Since the division terminates and does not repeat, 31/40 can be expressed as a terminating decimal.
To summarize, the rational numbers that can be expressed as repeating decimals are 5/12. The other numbers, 7/8, 17/25, and 31/40, can be expressed as terminating decimals.