Which of the following rational numbers can be expressed as a repeating decimal: 7/8, 5/12, 17/25, or 31/40?
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yall the answer is 5/12 trust me
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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)
0.538461
Convert 0.8¯¯¯ to a rational number.(1 point)
8/9
To convert 0.82¯¯¯¯¯ to a rational number, you would set x equal to 0.82¯¯¯¯¯ and then multiply both sides of the equation by what number?(1 point)
100
How do you show the group of digits that repeat in a repeating decimal? (1 point)
Responses
by underlining them
by putting them in parentheses
by putting a bar over them
by printing them in italics
To determine which of the given rational numbers can be expressed as a repeating decimal, we need to look for patterns in the decimals of the quotients.
To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). Let's perform the divisions:
1. 7/8 = 0.875
2. 5/12 = 0.4166...
3. 17/25 = 0.68
4. 31/40 = 0.775
Now, let's analyze each decimal to identify any repeating patterns:
1. 0.875: This decimal terminates, meaning it ends without repeating digits. Therefore, 7/8 cannot be expressed as a repeating decimal.
2. 0.4166...: The decimal repeats the digit '6'. Hence, there is a repeating pattern, making 5/12 a repeating decimal.
3. 0.68: This decimal terminates. Thus, 17/25 does not produce a repeating decimal.
4. 0.775: The decimal repeats the digit '7'. Hence, there is a repeating pattern, making 31/40 a repeating decimal.
In conclusion, the rational numbers that can be expressed as repeating decimals are 5/12 and 31/40.
In order to determine if a rational number can be expressed as a repeating decimal, we need to determine if the denominator can be expressed as a power of 2 or a power of 5. If the denominator can be factored into only 2's and 5's, then the decimal will terminate. Otherwise, the decimal will repeat.
The denominator of 7/8 is already factored into powers of 2, so the decimal will terminate. $\frac{7}{8} = 0.875$.
The denominator of 5/12 can be factored into $2^2$ and $3$ , so the decimal will repeat. $\frac{5}{12} = 0.41666666\ldots$.
The denominator of 17/25 can be factored into $5^2$, so the decimal will terminate. $\frac{17}{25} = 0.68$.
The denominator of 31/40 can be factored into $5 \cdot 2^3$, so the decimal will repeat. $\frac{31}{40} = 0.775$.
Therefore, of the given rational numbers, $\boxed{\frac{5}{12}}$ and $\boxed{\frac{31}{40}}$ can be expressed as repeating decimals.