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.
(1 point)
7/13 as a repeating decimal is 0.538461 with the 6 repeating.
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To express 7/13 as a repeating decimal, you can follow these steps:
1. Perform long division: Divide 7 by 13. Write down the whole number part of the quotient (which is 0) and the remainder (which is 7).
0.
_______
13 | 7.000
- 0
---
7
2. Multiply the remainder (7) by 10 to bring down the next digit. Divide the result by 13, and repeat the process.
0.5
_______
13 | 7.000
- 0
---
7
- 6
---
10
3. Repeat step 2 until you obtain a repeating pattern or until the numbers stop repeating.
0.538461538461...
Once you notice the pattern repeating, you can mark it with a bar over the digits that repeat. In this case, the digits 538461 repeat, so writing it as a repeating decimal, the answer is:
7/13 = 0.538461̅
Convert 0.8¯¯¯ to a rational number.(1 point)
To convert 0.8¯¯¯ to a rational number, we can use the fact that 0.8¯¯¯ is equivalent to 0.8888... (since the digit 8 repeats indefinitely).
Let's represent 0.8¯¯¯ as the variable x.
x = 0.8¯¯¯
Now, we multiply both sides of the equation by 10, which allows us to shift the decimal point one place to the right:
10x = 8.8¯¯¯
Next, we subtract the original equation from the new equation, to eliminate the repeating decimals:
10x - x = 8.8¯¯¯ - 0.8¯¯¯
9x = 8
Finally, we divide both sides of the equation by 9:
x = 8/9
Therefore, the rational number equivalent to 0.8¯¯¯ is 8/9.
To express 7/13 as a repeating decimal, we need to divide 7 by 13.
7 ÷ 13 = 0.53846153846153846153846153846154...
The repeating decimal representation of 7/13 is 0.53846153846153846153846153846154... with the digits 538461 repeating.
To express 7/13 as a repeating decimal, we need to perform long division.
First, we write 7 as the numerator and 13 as the denominator:
0.538461538461538461...
To mark the repeating digits with a bar, we place a bar above the digits that repeat. In this case, the digits 538461 repeat:
0.5 3 8 4 6 1 |
----------------------
13) 7
Next, we perform long division:
0.5 3 8 4 6 1 |
----------------------
13) 7
We divide 7 by 13:
0.5 3 8 4 6 1 |
----------------------
13) 7.0
The quotient is 0.538461538461538461..., and the bar is placed above the repeating digits.
Therefore, 7/13 as a repeating decimal is approximately 0.538461538461538461...