Question

write the number 10/27 as a repeating decimal. (note: on moodle it is difficult to create the line above your repeating value so simply add the phrase repeating after your dec)

Explanation:

Step1: Divide 10 by 27

To convert the fraction $\frac{10}{27}$ to a decimal, we perform the division: $10 \div 27$.
When we divide 10 by 27, we get:

$$
LATEXBLOCK0
$$

We can see that the sequence "370" repeats indefinitely.

Step2: Identify the repeating part

The repeating cycle here is "370" because it repeats continuously after the decimal point. So, we can write $\frac{10}{27}$ as $0.\overline{370}$, where the bar is placed over the repeating digits.

Answer:

$0.\overline{370}$ (or $0.370370\cdots$ with the phrase "repeating" to indicate the repeating part is 370)