Question

Layla skated x kilometers. Lamel skated
5
2
​
less than Layla. We can use the equation y=
5
3
​
x to represent this distance. Write
5
3
​
in decimal form.
You can use long division to write
5
3
​
as a decimal. Divide 30 tenths by 5 on the algorithm to find the decimal equivalent.
0 .

5 3 .0

.
.

Answer 1

To convert the fraction \( \frac{5}{3} \) into decimal form using long division, we will divide 5 by 3.

1. **Set up the long division**:
- 3 goes into 5 one time (1) with a remainder of 2.
- The result so far is 1.

2. **Add a decimal point and zeros**:
- You can bring down a 0, making it 20.
- Now, divide 20 by 3.

3. **Continue with the division**:
- 3 goes into 20 six times (6) because \( 3 \times 6 = 18 \).
- Subtract 18 from 20, leaving a remainder of 2.
- The result so far is now 1.6.

4. **Repeat the process**:
- Bring down another 0, making it 20 again.
- Divide 20 by 3 again to get 6.
- This process will continue indefinitely, reinforcing that \( 3 \) divides into \( 20 \) six times repeatedly.

Hence, we can conclude that:

\[
\frac{5}{3} = 1.666\ldots
\]

Thus, in decimal form:

\[
\frac{5}{3} \approx 1.67 \text{ (rounded to two decimal places)}
\]

So, the answer to your question is:

\[
0.666\ldots \text{ (or equivalently, } 1.\overline{6} \text{)}
\]