Question

problem 1
finish writing \\(\frac{3}{8}\\) as a decimal.
use the sketch tool or paper if it helps you with your thinking.
0.3
is the decimal representation of \\(\frac{3}{8}\\) terminating or repeating?
terminating repeating

Explanation:

Part 1: Finish writing \(\frac{3}{8}\) as a decimal

Step1: Continue the division

After subtracting 24 from 30, we get a remainder of \(30 - 24 = 6\). We add a zero to make it 60 (since we're dealing with decimals, we can add zeros after the decimal point). Now, we divide 60 by 8. \(8\times7 = 56\), so we write 7 next to the 3 in the decimal place.
\(60 - 56 = 4\). Add another zero to make it 40. Divide 40 by 8, \(8\times5 = 40\), so we write 5 next to the 7.

Step2: Combine the decimals

We had 0.3 initially, then we added 0.07 and 0.005. So \(0.3 + 0.07 + 0.005 = 0.375\).

A terminating decimal is a decimal that has a finite number of digits after the decimal point. Since \(\frac{3}{8}=0.375\), which has only three digits after the decimal point and no repeating pattern, it is a terminating decimal.

Answer:

0.375

Part 2: Is the decimal representation of \(\frac{3}{8}\) terminating or repeating?