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.
To express 7/13 as a repeating decimal and mark the repeating digits with a bar, we can perform long division.
Let's proceed with the long division process:
___0.
13 | 7.000000000000
- 6
-----
10
- 9
-----
10
- 9
-----
10
- 9
-----
10
- 9
-----
...
In this case, the division does not terminate, and the digits 9 and 0 repeat indefinitely.
Hence, the decimal representation of 7/13 is 0.538461538461..., and the repeating digits, marked with a bar, are 538461.
Therefore, 7/13 can be expressed as 0.538\(\overline{461}\).
redo it, its wrong
Apologies for the mistake. Let's correctly express 7/13 as a repeating decimal and mark the repeating digits with a bar.
Now, let's perform the long division:
0.53846153846...
-----------------
13 | 7.00000000000
- 6
-----------
10
- 9
-----------
10
- 9
-----------
10
- 9
-----------
...
The division continues indefinitely without repeating the same remainder. In this case, we can observe that the remainder after each subtraction is not repeating. Therefore, 7/13 is a decimal that does not repeat.
The decimal representation of 7/13 is 0.53846153846..., and it doesn't have a repeating pattern.
Convert 0.8¯¯¯
to a rational number
To convert the repeating decimal 0.8¯¯¯ to a rational number, we can set up an equation to solve for the unknown number.
Let x = 0.8¯¯¯
Since the bar is above the digit 8, it means that the digit 8 repeats indefinitely.
Multiplying the equation by 10 to shift the decimal point:
10x = 8.¯¯¯
Subtracting the original equation from the multiplied equation to eliminate the repeating decimals:
10x - x = 8.¯¯¯ - 0.8¯¯¯
9x = 8
Solving for x:
x = 8/9
Therefore, the rational number equivalent to the repeating decimal 0.8¯¯¯ is 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?
To convert the repeating decimal 0.82¯¯¯¯¯ to a rational number, we can set up an equation as follows:
Let x = 0.82¯¯¯¯¯
To eliminate the repeating decimals, we need to multiply both sides of the equation by a suitable power of 10.
In this case, we need to multiply by 100, since there are two digits repeating.
Multiplying both sides by 100:
100x = 82.82¯¯¯¯¯
Therefore, to convert 0.82¯¯¯¯¯ to a rational number, we would multiply both sides of the equation by 100.
How do you show the group of digits that repeat in a repeating decimal?(1 point)
Responses
by putting a bar over them
by putting a bar over them
by printing them in italics
by printing them in italics
by putting them in parentheses
by putting them in parentheses
by underlining them
The correct response is: by putting a bar over them.
How many digits long could the repeating cycle of a repeating decimal be if the denominator of the rational number is 7?(1 point)
Responses
infinitely long
infinitely long
up to six digits long
up to six digits long
any finite length
any finite length
up to seven digits long