Start at the biggest place. The first place where the digits differ decides everything.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Match the places first
Compare 0.4 and 0.386 by writing 0.400. Then 4 against 3 settles it.
Length still does not decide
0.9 beats 0.1234, even though the second has far more digits.
Step 2: Try It Yourself
Tap and try it out.
40/100 = 0.40 = 0.4
38/100 = 0.38
0.4 covers more squares than 0.38, so it is greater.
The whole is cut into 4 equal shares, called fourths.
1/4 shaded
1 of 4 shares is shaded. That is one fourth.
Step 3: In Real Life
A swimming final
Two swimmers touch at 47.845 and 47.851 seconds. Compare the biggest place first. Same, same, same, then 4 beats 5. The first swimmer wins by six thousandths.
Step 4: Watch an Example
One step at a time.
Watch Leo Order Three Decimals
Leo orders 0.7, 0.68, and 0.702.
- Step 1
He writes them all to three places: 0.700, 0.680, 0.702.
Step 5: Your Turn
Practice makes it stick.
The Times
Problem 1 of 2
Which is faster, a time of 9.85 seconds or 9.9 seconds?
The Weights
Problem 2 of 2
Which is heavier, 2.305 kg or 2.35 kg?
Which Is Bigger?
1 of 4
Which is bigger, 0.5 or 0.462?
2 of 4
Which is bigger, 0.207 or 0.27?
3 of 4
Which is bigger, 0.9 or 0.1234?
4 of 4
Which place do you compare first?
Cut the Whole
Build it, then check.
Cut the shape into 4 equal parts.
The whole is cut into 2 equal shares, called halves.
0/2 shaded
Step 6: Quick Check
Show what you know.
Question 1 of 2
Which is bigger, 0.608 or 0.61?
Question 2 of 2
Does a decimal with more digits have to be bigger?
What You Learned
- Write both decimals to the same number of places.
- Compare from the biggest place, moving right.
- The first place where they differ decides.
For the grown-up
This lesson is where the child compares and orders decimals to thousandths and justifies the order. The pattern that built whole numbers continues to the right of the decimal point without changing. Each place is a tenth of the one before, which is the same rule read the other way.
Watch for the decimal point being treated as a separator between two whole numbers. It is a marker for where the ones place ends, nothing more.
Say the place names aloud: three and four tenths, not three point four. The words carry the structure that the notation hides.
Compare place by place from the left — For 0.472 against 0.48, look at tenths: 4 and 4, equal. Hundredths: 7 against 8. Eight hundredths beats seven, so 0.48 is larger. The first difference from the left settles it, and nothing to the right can overturn it.
Padding makes it obvious — Write 0.48 as 0.480 and compare 472 thousandths with 480 thousandths. Padding with zeros puts both numbers in the same unit, which is the same move as finding a common denominator. It costs nothing and removes all doubt.
More digits is still not bigger — 0.472 has three digits and 0.48 has two, yet 0.48 is larger. The whole-number instinct that longer means bigger fails completely for decimals. If you catch yourself reaching for it, pad and compare as counts instead.
Ordering a list — Pad every number to the same number of decimal places first, then order them as if they were whole numbers. Doing the padding for all of them up front is far more reliable than comparing pairs one at a time and hoping the order is consistent.
Pad them to the same length — Compare 0.4 and 0.386. Write 0.4 as 0.400. Now both are thousandths. 400 against 386. 0.4 is bigger. More digits does not mean a bigger number. It means finer pieces.