Express 7/11

Question

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.

Show your work.

(1 point)

Answer 1

To express \( \frac{7}{11} \) as a repeating decimal, we can perform long division.

1. Divide 7 by 11. Since 7 is less than 11, we start by placing a decimal point and adding a zero: \[ 7.0000 \div 11 \]

2. 11 goes into 70 six times since \( 11 \times 6 = 66 \).

   • Write down 6 in the quotient.
   • Subtract 66 from 70: \[ 70 - 66 = 4 \]

3. Bring down another 0, making it 40.

   • 11 goes into 40 three times since \( 11 \times 3 = 33 \).
   • Write down 3 in the quotient.
   • Subtract 33 from 40: \[ 40 - 33 = 7 \]

4. Bring down another 0, making it 70 again.

   • As before, 11 goes into 70 six times.
   • Write down 6 in the quotient.
   • Subtract 66 from 70: \[ 70 - 66 = 4 \]

At this point, we can see that the digits "63" are repeating: \( 6 \) is paired with \( 3 \).

Thus, \( \frac{7}{11} \) can be expressed as: \[ 0.\overline{63} \]

In conclusion, the repeating decimal representation of \( \frac{7}{11} \) is \( 0.\overline{63} \).

Answer 2

in words

Answer 3

To express the fraction seven elevenths (\( \frac{7}{11} \)) as a repeating decimal, we start by dividing seven by eleven using long division.

First, since seven is less than eleven, we place a decimal point, making it seven point zero. This allows us to work with larger numbers by adding a zero to the dividend. Now, we divide seventy (from seven point zero) by eleven. Eleven goes into seventy six times, which equals sixty-six. We write six in the quotient and subtract sixty-six from seventy, resulting in four.

Next, we bring down another zero, turning our four into forty. Now, we see how many times eleven fits into forty. It fits three times, which is thirty-three. We write three in the quotient and subtract thirty-three from forty, leaving us with seven.

Then, we bring down another zero to make it seventy again. We notice that this process will repeat, as eleven goes into seventy exactly six times again. This sequence continues, oscillating between the numbers six and three.

Therefore, we find that the repeating decimal representation of seven elevenths is zero point six three, with the digits six and three repeating indefinitely. We write this as \( 0.\overline{63} \), indicating that the six and three form a repeating sequence.

Answer 4

words and number's

Answer 5

To express the fraction seven elevenths (7/11) as a repeating decimal, we perform the long division of 7 by 11.

1. Since seven is less than eleven, we start by placing a decimal point in the quotient, which gives us seven point zero (7.0).

2. Next, we consider seventy (70)—after adding a zero. Eleven goes into seventy six times because 11 times 6 equals 66. We write the number 6 in the quotient.

3. Now, we subtract 66 from 70, which leaves us with 4.

4. We then bring down another zero, making it 40. Now we check how many times eleven fits into forty. It fits three times because 11 times 3 equals 33. We write the number 3 in the quotient.

5. We subtract 33 from 40, which leaves us with 7.

6. Once again, we bring down another zero to make it seventy (70). We notice this is the same situation we started with, where eleven goes into seventy six times (just like before).

This cycle continues between the digits 6 and 3.

Thus, we find that the decimal representation of seven elevenths (7/11) is zero point six three, repeating. We write this as 0.63 with a bar over the numbers 6 and 3 to indicate they repeat indefinitely.

In conclusion, \( \frac{7}{11} = 0.\overline{63} \).