A number with more digits is bigger. 10,000 beats 9,999 without any further work.
Step 1: Picture It
Start with something you already know.
Putting words in ABC order
- To order "cart" and "cast", start at the first letter.
- The first letters match, and so do the second.
- Then r comes before s, and you can stop.
Compare numbers the same way: from the left, to the first difference.
Where the picture stops: first count the digits. More digits is bigger.
Step 2: Let's Learn
Read it, or press Listen and follow the words.
Try it first
Ana has 2,850 stickers. Leo has 2,390. Who has more hundreds?
Stuck is fine. Let’s Learn shows the way next. Got it first time? You can jump ahead to Watch an Example.
Same number of digits
Then compare from the left, one place at a time, until you find a difference.
The first difference decides
In 45,231 and 45,198, the thousands tie. The hundreds do not: 2 beats 1.
Step 3: Try It Yourself
Tap and try it out.
Left
Right
452 is greater than 419.
Step 4: In Real Life
Two house prices
One house costs 385,000 dollars. Another costs 372,000. Start at the left. The hundred thousands match. Then 8 beats 7. The first house costs more.
Step 5: Watch an Example
One step at a time.
Watch Ana Compare 6,408 and 6,480
Ana compares 6,408 and 6,480. Both have four digits.
- Step 1
Ana counts the digits. Both have four, so she looks closer.
Watch Maya Compare 8,362 and 8,371
Maya compares 8,362 and 8,371. Maya starts, and you finish.
- Step 1
Maya counts the digits. Both have four, so she looks closer.
Step 6: Your Turn
Practice makes it stick.
Two Trucks
Problem 1 of 12
A red truck costs $7,050. A blue truck costs $7,500. Which price is bigger, in dollars?
dollars
The School Van
Problem 2 of 12
A van costs $19,999. A minibus costs $20,100. Which price is bigger, in dollars?
dollars
Which Is Bigger?
Count the digits first. Then compare from the left.
Problem 3 of 12
Which is bigger, 46,200 or 41,900?
Problem 4 of 12
Which is bigger, 160,050 or 106,500?
Problem 5 of 12
Which sign belongs between 7,905 and 7,950?
Find the Mistake
One line on each page is a slip. Find it, then fix it.
Problem 6 of 12
Sam compares 5,491 and 5,530. One line is a slip. Which?
Sam's answer for: which is bigger, 5,491 or 5,530?
- 15,491 and 5,530: four digits each
- 2The ones decide: 1 beats 0
- AnswerSo 5,491 > 5,530
Problem 7 of 12
Which of Sam's two numbers is really bigger?
Problem 8 of 12
Maya compares 9,845 and 10,200. One line is a slip. Which?
Maya's answer for: which is bigger, 9,845 or 10,200?
- 19,845 has four digits. 10,200 has five.
- 2The first digits are 9 and 1
- AnswerSo 9,845 > 10,200
Problem 9 of 12
Which of Maya's numbers is bigger?
Which Way?
Pick the way that starts right.
Problem 10 of 12
Priya compares 7,600 and 7,060. Which way starts right?
Problem 11 of 12
To compare 4,210 and 990, which way is quicker?
Build Both Numbers
Build it, then check.
Problem 12 of 12
Priya has 4 hundreds, 8 tens and 2 ones. Leo has 4 hundreds, 2 tens and 8 ones. Build Priya on the left and Leo on the right.
Priya
Nothing.
Leo
Nothing.
0 is equal to 0.
Step 7: Quick Check
Show what you know.
Question 1 of 2
Which is bigger, 32,450 or 32,405?
Question 2 of 2
Where do you start comparing?
Ready for more?Optional. Past the lesson, for anyone who wants it.
Stretch 1 of 2
A number is bigger than 4,500 and smaller than 4,520. Its tens digit is 1. What is the biggest it can be?
Stretch 2 of 2
Leo's number is 7,3?6. The ? is one missing digit. Priya's number is 7,352. What is the biggest digit for ? that keeps Leo's number smaller?
What You Learned
- More digits means a bigger number.
- Otherwise compare from the left.
- The first place where they differ decides it.
For the grown-up
This lesson is where the child compares multi-digit numbers using >, <, and =. Each place is ten times the one to its right, and that single rule generates the whole system all the way to a million and, later, all the way down past the decimal point.
Watch for large numbers read digit by digit. "Four hundred and seven thousand" is a structure; "four zero seven" is a phone number.
Have them say the number aloud before working with it. Most errors with big numbers are reading errors that the arithmetic then faithfully preserves.
The slip this lesson targets is comparing from the wrong end: Sam reads the ones first and makes 5,491 beat 5,530. Ask which place is worth the most, and start the comparison there. Two others to watch: Maya's, where the leading digits of numbers of different lengths are set against each other — the 9 in 9,845 against the 1 in 10,200 — so the digits have to be counted before anything is compared; and stopping too early, where a tie in one place is read as a tie overall. The first place where the digits differ decides, and nothing to the right of it can change the answer.
Start at the left, stop at the first difference — To compare 348,275 and 348,527, run along from the left: 3=3, 4=4, 8=8, 2 against 5. The first difference decides it, so 348,527 is larger. Everything to the right of that point is irrelevant, however large it looks.
Count the digits first — A six-digit number always beats a five-digit one, because it has a hundred-thousands place and the other does not. Comparing lengths first can settle the question before you look at any digit at all.
Line them up to compare — Writing the two numbers one above the other, with their ones digits aligned, makes the comparison visual. Misalignment is the main source of error here — a digit that appears to be in the thousands column may actually be in the hundreds.
Ordering several numbers — To put a list in order, first sort by number of digits, then compare within each group from the left. Working systematically beats comparing pairs at random, which is how numbers get missed or placed twice.
Biggest place first, then stop — Compare 45,678 and 45,912. Ten-thousands: 4 and 4. Tie. Thousands: 5 and 5. Tie. Hundreds: 6 against 9. Nine wins. 45,912 is bigger, and nothing to the right of that mattered. You stop at the first place where they differ.