Question

Express 7/11 as a repeating decimal. Mark the cycle of repeating digits with a bar.

Answer 1

To convert the fraction \( \frac{7}{11} \) into a decimal, we can perform the division:

1. Divide 7 by 11.

Starting with \( 7.000000 \):

- \( 11 \) goes into \( 70 \) six times (since \( 11 \times 6 = 66 \)).
- Subtract \( 66 \) from \( 70 \) to get \( 4 \).
- Bring down the next \( 0 \) to get \( 40 \).
- \( 11 \) goes into \( 40 \) three times (since \( 11 \times 3 = 33 \)).
- Subtract \( 33 \) from \( 40 \) to get \( 7 \).
- Bring down the next \( 0 \) to get \( 70 \), and we are back to where we started.

This process shows that the decimal will continue to repeat. Therefore, we have:

\[
\frac{7}{11} = 0.636363\ldots
\]

We can denote this repeating decimal by using a bar over the repeating digits:

\[
\frac{7}{11} = 0.\overline{63}
\]

Thus, the final answer is:

\[
\frac{7}{11} = 0.\overline{63}
\]

Answer 2

answer this like a human

Answer 3

Sure! To express \( \frac{7}{11} \) as a repeating decimal, you can start by dividing 7 by 11.

When you perform the division, you'll find that:

- 11 goes into 70 (after placing a decimal point and adding zero) six times, which gives you 66.
- This leaves you with a remainder of 4.
- When you bring down the next zero, you get 40, and 11 goes into 40 three times, totaling 33.
- This gives you another remainder of 7, and when you bring down another zero, you’re back to the original 70.

This cycle continues, leading us to see that the decimal form keeps repeating the digits "63."

So, \( \frac{7}{11} \) can be represented as the repeating decimal:

\[
0.\overline{63}
\]

The bar over "63" indicates that these two digits will continue infinitely.

Answer 4

without the frac things and use less details

Answer 5

Sure!

When you divide 7 by 11, you get a repeating decimal:

0.636363...

To show that "63" repeats, we write it as:

0.\overline{63}

So, 7 divided by 11 is 0.\overline{63}.

Answer 6

without the overline things too, make it seems like a 8th grader wrote this

Answer 7

Got it!

When you divide 7 by 11, you get 0.636363... and the "63" keeps repeating forever.

So, you can say that 7 divided by 11 equals 0.636363... with "63" repeating.