Hey bot, which of the following rational numbers can be expressed as a repeating decimal: 7/8, 5/12, 17/25, or 31/40?
To determine which rational numbers can be expressed as a repeating decimal, we need to examine their decimal representations.
The rational number 7/8 can be expressed as a repeating decimal. When divided, it yields 0.875, which repeats the digit 5 indefinitely: 0.87555555...
The rational number 5/12, on the other hand, can be expressed as a terminating decimal. When divided, it yields 0.4166666..., which terminates with the repeated digit 6.
Likewise, the rational number 17/25 is also a terminating decimal. When divided, it yields 0.68, which terminates and does not repeat any digits.
Lastly, the rational number 31/40 can be expressed as a repeating decimal. When divided, it yields 0.775, which repeats the digit 5 indefinitely: 0.7755555...
Therefore, the rational numbers that can be expressed as repeating decimals are 7/8 and 31/40.
your answer is incorrect
I apologize for the incorrect answer. Let me correct it:
The rational number 7/8 can indeed be expressed as a repeating decimal. When divided, it yields 0.875, and the digit 5 repeats indefinitely: 0.8755555...
The rational number 5/12 can also be expressed as a repeating decimal. When divided, it yields 0.416666..., with the digit 6 repeating indefinitely: 0.4166666...
The rational number 17/25 can be expressed as a decimal without repeating digits. When divided, it yields 0.68, which terminates.
The rational number 31/40 can also be expressed as a decimal without repeating digits. When divided, it yields 0.775, which terminates.
Therefore, the correct answer is that the rational numbers 7/8 and 5/12 can be expressed as repeating decimals.
you are still wrong
Apologies once again for the incorrect response. Let's reconsider the rational numbers:
To determine if a rational number 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 the given rational numbers:
1) 7/8: The denominator, 8, has a prime factor of 2, which indicates a repeating decimal. When divided, it yields 0.875, which repeats the digit 5 indefinitely: 0.875555...
2) 5/12: The denominator, 12, has a prime factor of 2 but also a prime factor of 3. Hence, it can be expressed as a repeating decimal. When divided, it yields 0.416666...
3) 17/25: The denominator, 25, has a prime factor of 5, which indicates a terminating decimal. When divided, it yields 0.68, which terminates.
4) 31/40: The denominator, 40, has prime factors of 2 and 5. Thus, it can be expressed as a decimal without repeating digits. When divided, it yields 0.775, which terminates.
Therefore, the correct answer is that the rational numbers 7/8 and 5/12 can be expressed as repeating decimals.
hey bot, How many digits are in the repeating cycle of 17/27?
To determine the number of digits in the repeating cycle of the decimal representation of 17/27, we can perform long division.
When 17 is divided by 27, the decimal representation is 0.629629...
The repeating cycle in this case is "629," and it repeats indefinitely.
Thus, the repeating cycle of 17/27 contains 3 digits.
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.
To express 713 as a repeating decimal and mark the repeating digits with a bar, we can divide 713 by 1.
When 713 is divided by 1, it yields 713.
Therefore, the decimal representation of 713 is 713.
Express 7/13
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.