Express the fractions 3/8 and 1/10 as decimals. What are their decimal representations?

Introduction:
This question evaluates your ability to convert two simple fractions, 3/8 and 1/10, into decimal form. Such conversions are used heavily in percentage calculations, ratio problems, and financial mathematics.

Given Data / Assumptions:

• Fractions: 3/8 and 1/10.
• We must express each as a decimal.
• The answers should be exact, terminating decimals.

Concept / Approach:
For each fraction a/b, we convert to decimal by performing the division a ÷ b. Since 8 and 10 are composed of factors 2 and 5, both 3/8 and 1/10 have terminating decimal expansions. We can compute them directly or recall well-known fraction–decimal pairs.

Step-by-Step Solution:
Step 1: Convert 3/8 to a decimal: 3 ÷ 8.Step 2: Perform the division: 8 goes into 30 three times (3 * 8 = 24), remainder 6; bring down a 0 to make 60.Step 3: 8 goes into 60 seven times (7 * 8 = 56), remainder 4; bring down a 0 to make 40.Step 4: 8 goes into 40 five times (5 * 8 = 40), remainder 0.Step 5: The quotient is 0.375, so 3/8 = 0.375.Step 6: Convert 1/10 to a decimal: 1 ÷ 10 = 0.1, because moving the decimal point one place left divides by 10.Step 7: Therefore, the decimal representations are 0.375 and 0.1.

Verification / Alternative check:
Write them as fractions with denominators that are powers of 10. For 3/8, multiply numerator and denominator by 125: 3/8 = (3 * 125)/(8 * 125) = 375/1000 = 0.375. For 1/10, it is already one tenth, so directly 0.1. These match our division results exactly.

Why Other Options Are Wrong:
0.375 and 1 implies 1/10 equals 1, which is incorrect. 1.375, 13.75, and 1.1 are far from the true values and come from misplacing decimal points. 0.3 and 0.1 would correspond to 3/10 and 1/10, not 3/8 and 1/10. Only the pair 0.375 and 0.1 correctly represents 3/8 and 1/10.

Common Pitfalls:
Students sometimes mix up 3/8 with 3/10 or 1/8, or incorrectly perform the division 3 ÷ 8, leading to wrong decimals. Another error is to assume 1/10 is 0.01 rather than 0.1. Remember that dividing by 10 shifts the decimal one place to the left, not two places.

Final Answer:
The decimal forms are 3/8 = 0.375 and 1/10 = 0.1.