Questions: Converting Between Fractions, Decimals, and Percents

Question 1

A student converts 3/4 to a percent for a report on interest rates and writes '0.75%.' Why is this a significant error?

• A. It is not an error — 3/4 and 0.75% represent the same quantity
• B. The student moved the decimal in the wrong direction; 3/4 = 75%, not 0.75%
• C. Fractions cannot be directly converted to percents without using the midpoint formula
• D. The error is only stylistic — the value is correct but the notation is unusual

Answer: (B)

3/4 = 0.75 as a decimal, and converting to percent means multiplying by 100 (shifting the decimal two places right), giving 75%. Writing 0.75% would mean 0.75 per hundred, which equals 0.0075 — an entirely different quantity. In a real context like interest rates, this error is enormous: a 75% rate versus a 0.75% rate are very different financial realities.

Question 2

A savings account advertisement says it pays '0.5% annual interest.' A student calculates the annual interest on a $400 deposit as $200. What went wrong?

• A. Nothing — 0.5% of $400 is indeed $200
• B. The student treated 0.5% as 0.5 (one-half) instead of 0.005 (one-half of one percent)
• C. The student should have divided by 100 before multiplying, not after
• D. Percents cannot be applied to dollar amounts without a unit conversion

Answer: (B)

0.5% means 0.5 per hundred, which as a decimal is 0.005. Multiplying $400 × 0.005 = $2.00. The student treated '0.5%' as though it were '0.5' (the decimal for 50%), computing $400 × 0.5 = $200. This is the classic magnitude error: confusing a number (0.5) with that same number expressed as a percent (0.5%). These differ by a factor of 100.

Question 3

The decimal 0.333... (with 3 repeating infinitely) is not exactly equal to 1/3 — it is mainly an approximation.

• T. True
• F. False

Answer: False

0.333... with the 3 repeating infinitely is exactly equal to 1/3. Repeating decimals are not approximations — they are the complete, exact decimal representation of fractions whose denominators have prime factors other than 2 and 5. The confusion arises because we often round 1/3 to 0.33 for practical purposes, but that rounded value is the approximation. The infinite repeating decimal is the exact equivalent.

Question 4

To convert 0.25% to a fraction, you write it as 1/4.

• T. True
• F. False

Answer: False

0.25% means 0.25 per hundred, which equals 0.0025 as a decimal, which equals 25/10000 = 1/400 — not 1/4. The fraction 1/4 equals 25%, not 0.25%. This is the core magnitude trap: the number 0.25 and the percent 0.25% look similar but differ by a factor of 100. Always complete the full conversion: percent → decimal (divide by 100) → fraction.

Question 5

A classmate tells you that converting fractions to percents is just 'moving the decimal point.' What is missing from this explanation, and what is the complete correct process?

Model answer: Moving the decimal handles converting between decimals and percents, but it is only one step. To convert a fraction to a percent: first divide the numerator by the denominator to get a decimal (3/4 = 0.75), then multiply by 100 by shifting the decimal two places right (0.75 → 75%). The missing piece is the first step — dividing numerator by denominator — and the direction matters: shift right (multiply by 100) to go decimal→percent, shift left (divide by 100) to go percent→decimal. Getting the direction wrong is the most common error.

Percent literally means 'per hundred,' so multiplying by 100 converts a decimal into its equivalent 'per hundred' expression. Understanding why the rule works prevents reversing it.