Start at the biggest place. The first place where the digits differ decides everything.
Step 1: Picture It
Start with something you already know.
Words in a dictionary
- A dictionary puts words in order one letter at a time.
- It checks the first letter, then the next.
- "Zoo" comes after "apple," even though it is shorter.
Decimals work the same way: the first place that differs decides.
Where it stops: 0.4 equals 0.40, but "to" is not "too."
Step 2: Let's Learn
Read it, or press Listen and follow the words.
Try it first
Which is bigger, 0.35 or 0.32?
Stuck is fine. Let’s Learn shows the way next. Got it first time? You can jump ahead to Watch an Example.
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 3: 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 4: 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 5: Watch an Example
One step at a time.
Watch Ana Order Three Decimals
Ana puts 0.6, 0.547 and 0.58 in order, smallest first.
- Step 1
Ana writes zeros on the end. Now each number has three places. This is called padding.
Watch Leo Compare 0.209 and 0.21
Leo compares 0.209 and 0.21. He starts, and you finish.
- Step 1
Leo lines up the places. Both have 2 tenths, so the tenths tie.
Step 6: Your Turn
Practice makes it stick.
The Three Lanes
Problem 1 of 12
Three swimmers finish. The fastest has the smallest time. Which lane won?
The Long Jump
Problem 2 of 12
Noor jumped farther than 0.75 m but less than 0.8 m. Which could be her jump?
Which Is Bigger?
Pad them to the same length. Then compare from the left.
Problem 3 of 12
Which is bigger, 0.7 or 0.65?
Problem 4 of 12
Which is bigger, 0.312 or 0.32?
Problem 5 of 12
Which is bigger, 0.5 or 0.478?
Find the Mistake
One line on each page is a slip. Find it, then fix it.
Problem 6 of 12
Dev compares 0.36 and 0.4. One line is a slip. Which?
Dev's page for 0.36 and 0.4
- 10.36 and 0.4
- 20.36 is 36 hundredths, 0.4 is 4 hundredths
- Answer36 hundredths beats 4 hundredths, so 0.36 is bigger
Problem 7 of 12
Which is bigger, 0.36 or 0.4?
Problem 8 of 12
Priya orders three numbers. One line is a slip. Which?
Priya's page for 0.9, 0.87 and 0.092
- 1Order 0.9, 0.87, 0.092 smallest first
- 2Padded: 0.900, 0.870, 0.920
- Answer0.870, then 0.900, then 0.920
Problem 9 of 12
Which is smallest: 0.9, 0.87 or 0.092?
Same Number?
Pick the one that says the same thing.
Problem 10 of 12
Which of these is the same as 0.6?
Problem 11 of 12
Which of these is the same as 0.450?
Just Beat It
Build it, then check.
Problem 12 of 12
Shade the fewest squares you can that still beat 0.4.
0/100 = 0.00 = 0.0
40/100 = 0.40 = 0.4
0.4 covers more squares than 0.0, so it is greater.
The number to beat
Step 7: 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?
Ready for more?Optional. Past the lesson, for anyone who wants it.
Stretch 1 of 2
A decimal has three places after the point. It must be smaller than 0.5. What is the biggest it can be?
Stretch 2 of 2
Cards 3, 0 and 7 fill the blanks in 0.___ . Use each card once. What is the smallest number you can make?
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.
The slip this lesson targets is "more digits means bigger". It comes straight from whole numbers, where 1234 really does beat 9, so it is a sensible rule being used one year past its life. Padding kills it: ask for both numbers as counts of thousandths before comparing anything. Priya's slip is the other one, padding at the front instead of the end, which turns 0.092 into 0.920. Ask where the zeros are allowed to go and why.
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.