0.1Decimals Lab

Why did fractions trade their form for a decimal point?

0.3 vs 0.25 — which is bigger? (But 25 is more than 3?)

A fraction rewritten in place value — the decimal.

Feel the why in three minutesFullscreen

Experiment

Hands-on experiment

Predict first — 0.3 vs 0.25: which is bigger?

Build a ribbon length

A 1m ribbon cut into ten parts gives 0.1; cut those again for 0.01. Turn both digits.

first place (by 0.1)2

second place (by 0.01)0

0.20

ribbon length · 2/10 + 0/100

Read more — why it exists · insights · common mistakes · formulasExpand ▾

Why

Why does this exist?

Fractions record amounts exactly but compare slowly. Which is bigger, 1/4 or 2/7? You can't see it — you must compute a common denominator first.

The solution was to extend the place-value system we already had past the point. The rule 'one step left = ×10' becomes 'one step right = ÷10' — and 0.1, 0.01, 0.001 were born.

With denominators unified to 10, 100, 1000, comparison happens at a glance and addition works in columns like whole numbers. Heights, weights, records, prices — the measuring world runs on decimals for this reason.

Insight

Insights from the video

“A decimal isn't a new number — it's a fraction's new outfit.”
0.25 and 1/4 are one number. The content (the amount) stays; only the notation changes to place value — so the key to decimals is always converting back to tenths and hundredths.

“The place-value rule doesn't change at the point.”
One step left ×10, one step right ÷10 — the decimal point isn't where the rule changes; it's just the marker showing where the ones place is.

Misconception

Common misconceptions

0.25 is bigger than 0.3 — because 25 beats 3.

✓

Decimals compare place by place. In the tenths place 3 > 2, so 0.3 wins. 0.3 = 0.30 = 30/100 while 0.25 = 25/100 — 'more digits' and 'bigger' are different things.

0.30 is bigger than 0.3 — it has an extra digit.

✓

They're the same number: 30/100 = 3/10. A trailing zero says 'measured more precisely'; it never changes the size — the same principle as 3/10 = 30/100 in fractions.

Formula

Writing it as math

What the ribbon experiment confirmed, in mathematical language.

What a decimal is

The first place after the point counts tenths; the second counts hundredths — place value continuing rightward by ÷10.

Fraction ↔ decimal translation

Make the denominator 10, 100, 1000… and the decimal reads itself. Two notations, one number.

The comparison rule

Compare from the highest place down. Trailing zeros change nothing — 3/10 = 30/100.

In Real Life

Where you meet it in real life

Race times

The 100m world record: 9.58 seconds — gold and silver split by 0.01s. The language of sports records is decimal.

Height and weight

175.5cm, 68.2kg — measurements always land between the marks, and decimals are how we write the in-between.

Prices and markets

An exchange rate of 1,398.50, a stock move of +0.75% — finance's basic unit lives in the second decimal place.

Fuel pumps and deli scales

34.7L of gas, 0.628kg of pork belly — meters and scales speak decimals, and unit-price × decimal-quantity runs every day.

Try Yourself

Test yourself

Q1Which is bigger: 0.7 or 0.68?Show answer ▾

Compare tenths: 7 > 6, so 0.7. Indeed 0.7 = 0.70 = 70/100 vs 0.68 = 68/100 — longer doesn't mean bigger.

Q2Convert 3/4 to a decimal.Show answer ▾

Make the denominator 100: 3/4 = 75/100 = 0.75. Or divide: 3 ÷ 4 = 0.75 — a fraction is a division, after all.

Q3What happens when you convert 1/3?Show answer ▾

0.3333… — it never ends, repeating 3s (a repeating decimal). Fractions whose denominator can't become 10, 100, 1000… don't terminate. And if an endless decimal never even repeats? That's the irrational numbers story.

Try answering yourself before revealing it — getting it wrong is where learning starts.

Connection