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 with a bar, we need to perform long division.
0.5384615384615...
__________________
13 | 7.00000000000
6 5
_______
3 50
3 24
_______
2 60
2 34
________
2 60
2 34
________
0
The division terminates at this point since we have already reached a remainder of 0.
Therefore, 7/13 as a repeating decimal is approximately 0.5384615384615... or 0.538(461).
Convert 0.8¯¯¯ to a rational number
To convert 0.8¯¯¯ to a rational number, we can express it as a fraction.
Let x = 0.8¯¯¯
Then, multiplying both sides by 10, we get:
10x = 8.8¯¯¯
Subtracting x from both sides, we have:
10x - x = 8.8¯¯¯ - 0.8¯¯¯
9x = 8
Dividing both sides by 9, we get:
x = 8/9
Therefore, 0.8¯¯¯ as a rational number 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 0.82¯¯¯¯¯ to a rational number, we set x equal to 0.82¯¯¯¯¯ and then multiply both sides of the equation by 100, as follows:
100x = 82.82¯¯¯¯¯
By subtracting x from both sides, we acquire:
100x - x = 82.82¯¯¯¯¯ - 0.82¯¯¯¯¯
99x = 82
Finally, we divide both sides by 99 to determine the value of x:
x = 82/99
Therefore, 0.82¯¯¯¯¯ as a rational number is 82/99.
How do you show the group of digits that repeat in a repeating decimal?(1 point)
Responses
by printing them in italics
by printing them in italics
by putting a bar over them
by putting a bar over them
by underlining them
by underlining them
by putting them in parentheses
by putting them in parentheses
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
up to six digits long
up to six digits long
any finite length
any finite length
infinitely long
infinitely long
up to seven digits long
The correct response is:
up to six digits long
Convert 0.27¯¯¯¯¯
to a rational number in simplest form.(1 point)
Responses
127
Start Fraction 1 over 27 end fraction
27100
Start Fraction 27 over 100 end fraction
2799
Start Fraction 27 over 99 end fraction
311
To convert 0.27¯¯¯¯¯ to a rational number in simplest form, we follow these steps:
Let x = 0.27¯¯¯¯¯
Then, multiplying both sides by 100, we have:
100x = 27.27¯¯¯¯¯
Subtracting x from both sides, we obtain:
100x - x = 27.27¯¯¯¯¯ - 0.27¯¯¯¯¯
99x = 27
Dividing both sides by 99, we find:
x = 27/99
Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 9 in this case, we get:
x = 3/11
Therefore, 0.27¯¯¯¯¯ as a rational number in simplest form is 3/11.
To convert 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by what number?(1 point)
Responses
999
999
100
100
1,000
1,000
10
To convert 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by 1,000.
This is because we have three digits in the repeating cycle (264) and we need to shift the decimal point three places to the right to eliminate the repeating decimal.
Therefore, the correct response is:
1,000
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator? (1 point)
Responses
100
100
1,000
1,000
99
99
999
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with a denominator of 999.
The number of 9s in the denominator corresponds to the number of digits in the repeating cycle. In this case, since the repeating cycle has three digits, the denominator becomes 999.
Therefore, the correct response is:
999