How many digits are in the repeating cycle of 17/27?
To find the repeating cycle of a fraction, we need to perform long division.
Let's start by dividing 17 by 27:
0.6
_______
27| 17.0
- 16.2
______
8.8
As we can see, 17 divided by 27 gives us a quotient of 0.6, with a remainder of 8.8.
Next, we need to divide the remainder by 27.
0.6
_______
27| 17.0
- 16.2
______
8.8
- 8.1
______
7.0
We obtain a new quotient of 0.6, with a remainder of 7.0.
Since the remainder is now 7.0, and we have already encountered a remainder of 8.8, we can conclude that the decimal representation of 17/27 will contain a repeating cycle of length 2, which ends after the 8.8 segment.
Therefore, there are 2 digits in the repeating cycle of 17/27.
Express 7/13 as a repeating decimal.
To express 7/13 as a repeating decimal, we need to perform long division:
```
0.538461538461...
-----------------
13 | 7.000000000000...
- 6
--------
10
- 9
-----
10
- 9
-----
10
- 9
-----
...
```
As we can see, the remainder starts recurring as 10 - 9 - 10 - 9 - ... Thus, the repeating cycle in the decimal representation of 7/13 is 0.538461.
Therefore, 7/13 can be expressed as the repeating decimal 0.538461.
0.8 as a rational number
To express 0.8 as a rational number, we need to write it as a fraction in the form a/b, where a and b are integers.
The decimal 0.8 can be written as 8/10. However, we want to simplify this fraction to its simplest form.
We can simplify 8/10 by dividing both the numerator and the denominator by their greatest common divisor.
The greatest common divisor of 8 and 10 is 2. Therefore, we divide both 8 and 10 by 2:
8/2 = 4
10/2 = 5
So 8/10 simplifies to 4/5.
Therefore, 0.8 as a rational number is equal to 4/5.
0.8¯¯¯¯¯ as a rational number
To express the repeating decimal 0.8¯¯¯¯¯ as a rational number, we need to convert it into an equation and solve for the unknown variable.
Let x = 0.8¯¯¯¯¯.
To eliminate the repeating part, we multiply both sides of the equation by 10:
10x = 8.8¯¯¯¯¯
Next, we subtract the original equation from the newly obtained equation to eliminate the repeating part:
10x - x = 8.8¯¯¯¯¯ - 0.8¯¯¯¯¯
9x = 8
Finally, we can solve for x by dividing both sides of the equation by 9:
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 0.82¯¯¯¯¯ to a rational number, you would set x equal to 0.82¯¯¯¯¯ and then multiply both sides of the equation by 100.
Setting x = 0.82¯¯¯¯¯, we multiply both sides of the equation by 100:
100x = 82.82¯¯¯¯¯¯
By subtracting the original equation from the new equation, we can eliminate the repeating part:
100x - x = 82.82¯¯¯¯¯¯ - 0.82¯¯¯¯¯¯
99x = 82
Finally, we can solve for x by dividing both sides of the equation by 99:
x = 82/99
Therefore, the rational number equivalent to the repeating decimal 0.82¯¯¯¯¯ is 82/99.
How do you show the group of digits that repeat in a repeating decimal?(1 point)
by underlining them
by putting them in parentheses
by printing them in italics
by putting a bar over them