Express 711
as a repeating decimal. Mark the cycle of repeating digits with a bar.
Note: You will find the option to add a bar above text in the Geometry (∠
) keyboard.
(1 point)
The decimal representation of 711 as a repeating decimal is 0.711¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯+.
Express 7/11
as a repeating decimal. Mark the cycle of repeating digits with a bar.
Note: You will find the option to add a bar above text in the Geometry (∠
) keyboard.
(1 point)
To express 7/11 as a repeating decimal, we need to divide 7 by 11 using long division:
0.63
___________
11 | 7.00
We can see that 7 is less than 11, so we add a decimal point and a zero to the right of 7 and continue dividing:
0.63
___________
11 | 7.00
-66
____
40
- 33
____
70
-66
_______
40
The division is repeating between 63 and 40. Therefore, the decimal representation of 7/11 is 0.63¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯.
To express 711 as a repeating decimal, we can divide 711 by 9, which is the smallest number that can divide both 711 and 9 without a remainder.
When we divide 711 by 9, we get:
711 ÷ 9 = 79
So, 711 is equal to 79 with a remainder of 0. Therefore, the fraction form of 711 is 79/9.
Now, let's convert this fraction into a decimal. To do so, we divide 79 by 9:
79 ÷ 9 = 8 remainder 7
To continue the division, we add a decimal point after the 8 and bring down a zero:
79 ÷ 9 = 8.7
Since there is a remainder, we add a zero after the decimal point and continue the division:
70 ÷ 9 = 7 remainder 7
Again, we add a zero after the decimal point and bring down another zero:
70 ÷ 9 = 7.0
Now, we repeat the process:
0 ÷ 9 = 0 remainder 0
Since the remainder is zero, the division is complete. We can now express 711 as a repeating decimal:
711 = 79.777...
In this case, the repeating digits are 7, so we can write it as:
711 = 79.7¯¯¯
To express 711 as a repeating decimal, we can divide 711 by the number 99. The division would look like this:
711 ÷ 99 = 7.1818...
To express this as a repeating decimal, we can write it as: 7.18 with the digits 18 repeating.
In order to mark the repeating digits with a bar, we can write it as: 7.18̅.