Converting between percentages and decimals

Two-part: convert a decimal to a percent, and a percent to a decimal. Same trick, opposite directions.

01 Mini-Lesson Video

▸ VIDEO COMING SOON

A short walkthrough explaining what you need to know and how to solve this question type lands here once it's recorded.

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 v1

(a) Write 0.4 as a percentage.

0.4 =%

Percent to decimal v2

(b) Write 28.5% as a decimal.

28.5% =

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 How to Solve It

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.

0.4 to a percent (decimal → %).

The % sign means "out of 100," so to get there, multiply by 100. Multiplying by 100 shifts the decimal point two places to the right.

0.4 = 0.40 \to 40%

Tip: when you only see one digit after the decimal, picture the invisible trailing zero. 0.4 is really 0.40.

28.5% to a decimal (% → decimal).

Reverse direction: divide by 100, which shifts the decimal point two places to the left.

28.5% \to 0. 285

Walk it: 28.5 → 2.85 (one place) → 0.285 (two places). The decimal moved twice.

▸ COMMON SLIPS(1) Only moving one place. 0.4 becomes 4% instead of 40%. (2) Moving the wrong direction. 28.5% becomes 2,850 instead of 0.285. The fix: decimal-to-percent goes right (number gets bigger), percent-to-decimal goes left (number gets smaller). Always two places.

04 Practice — Step by Step

Three quick conversions. Different numbers from the ALEKS examples. Each step unlocks the next.

Decimal to percent.

Convert 0.7 to a percent. Type just the number (e.g. 50 for 50%).

answer =

Percent to decimal.

Convert 35% to a decimal.

answer =

Trickier: percent already has a decimal.

Convert 12.5% to a decimal.

answer =

▸ NICE WORK

You walked both directions of the conversion.

Same recipe every time: the decimal point moves two places. Going to a percent? Move right (the number gets bigger). Going to a decimal? Move left (the number gets smaller). ALEKS will mix and match the directions and the numbers. The move stays the same.

Topic overview Q2