0.3 vs 0.25 — which is bigger? (But 25 is more than 3?)
A decimal is a fraction rewritten in the place-value system — past the point, each step right is worth one tenth of the last.
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.
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.
Watch
Related video
Connection
Concepts connect
Previous concept
Fractions
Decimals are fractions' clothing — meet fractions first and the translation shows.
← Fractions labLeads to next
Repeating Decimals
1/3 = 0.333… never ends. How do we write an unending decimal — and walk it back to a fraction? — on to repeating decimals.
Go to the Repeating Decimals lab →Related
Labs worth exploring together
Related lab
Fractions
A decimal is a fraction's other notation — confirm the contents match first.
Go to the Fractions lab →Related lab
Irrational Numbers
Endless decimals with no repeat — the next story decimal notation leads to.
Go to the Irrational Numbers lab →