A number with more digits is bigger. 10,000 beats 9,999 without any further work.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
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 2: Try It Yourself
Tap and try it out.
Left
Right
452 is greater than 419.
Step 3: 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 4: Watch an Example
One step at a time.
Watch Ana Compare Two Big Numbers
Ana compares 45,231 and 45,198.
- Step 1
She counts the digits: five each, so that settles nothing.
Step 5: Your Turn
Practice makes it stick.
Two Cities
Problem 1 of 2
One town has 23,481 people and another has 23,900. Which number is bigger: 23,481 or 23,900?
Counting Digits
Problem 2 of 2
Which is bigger, 9,999 or 10,000?
Which Is Bigger?
1 of 3
Which is bigger, 54,321 or 54,231?
2 of 3
Which is bigger, 8,999 or 9,100?
3 of 3
Which is bigger, 70,000 or 69,999?
Show the Bigger Number
Build it, then check.
Which is bigger, 452 or 419? Put the marker on it.
Step 6: 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?
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.
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.