MAT-144 · Mathematical Reasoning
Topic 02 · Conversions & Budgeting
Converting between percentages and decimals
Two-part: convert a decimal to a percent, and a percent to a decimal. Same trick, opposite directions.
01
Worked Example Video
Every step of Converting between percentages and decimals explained on video. Pause anywhere; the embed scrolls independently of the page.
YOUTUBE
02
What This Looks Like on ALEKS
ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are two example versions you might see.
Decimal to percent
Write 0.4 as a percentage.
Type just the number (no % sign).
0.4 =
✓
Right — 0.4 = 40%. Picture the invisible trailing zero (0.40), then shift two places right → 40.
✗
0.4 = 0.40 (invisible zero). Shift the decimal two places right: 0.40 → 4.0 → 40. Answer: 40%.
Percent to decimal
Write 28.5% as a decimal.
28.5% =
✓
Right — 28.5% = 0.285. Two places left: 28.5 → 2.85 → 0.285.
✗
Percent-to-decimal moves the decimal two places left. 28.5 → 2.85 → 0.285.
Heads up: Your ALEKS version will use different numbers. The numbers in the practice below are different too — that way you're exercising the move, not memorizing one answer.
03
The Rule
decimal → percent
shift 2 places right (× 100)
percent → decimal
shift 2 places left (÷ 100)
Same number, two notations. The decimal point moves two places — never one. Going to a percent, the number gets bigger. Going to a decimal, the number gets smaller. See it live: fill 6 of 100 cells in the Percent Sandbox →
Common slip
Only moving one place. 0.4 becomes “4%” instead of 40%; 28.5% becomes “2.85” instead of 0.285. The move is always two places. When only one digit sits after the decimal (like 0.4), picture the invisible trailing zero: 0.40 → 40%.
04
Practice — Step by Step
Practice this problem step by step
Convert 0.06 to a percent.
Which direction?
You’re going decimal → percent. Which way does the decimal point move?
Going TO a percent means multiplying by 100 — so the number gets bigger, which means the decimal point moves right.
✓
Right. Decimal-to-percent means × 100, which shifts the decimal point two places right.
✗
Not quite — try again.
How many places?
How many places does the decimal move?
“Percent” literally means “per hundred.” Multiplying by 100 moves the decimal exactly two places.
✓
Right — two places, always. × 100 shifts exactly two decimal places.
✗
Not quite — try again.
Write the percent
Shift the decimal in 0.06 two places to the right. Type just the number (no % sign).
0.06 =
Slide the decimal two places right: 0.06 → 0.6 (one) → 6 (two).
✓
Perfect. 0.06 → 0.6 → 6, so 0.06 = 6%. Two places right, every time.
✗
Not quite. 0.06 = 0.06 shift right twice → 6. Answer: 0.06 = 6%.
🎉
You walked the conversion end to end.
Same recipe every time: the decimal point moves two places. Going to a percent? Right. Going to a decimal? Left. ALEKS mixes and matches directions — the move stays the same.