More digits means more
Which is more, 87 or 132? The 8 in 87 is bigger than the 1 in 132, but that does not decide it. 132 has three digits, so it has a hundred in it. 87 has only two digits, so it is less than 100.
Any 3-digit number is at least 100, and any 2-digit number is at most 99. So a number with more digits is always the larger one.
87 is 8 tens and 7 ones, with no hundred.
132 has a whole hundred, and that is already more than 87.
On a number line, 132 sits further to the right than 87, so 132 is larger.
Same number of digits: start at the left
When two numbers have the same number of digits, compare them place by place, starting with the biggest place on the left. Stop at the first place where the digits are different: that place decides.
Compare 340 and 390. Both have 3 hundreds, so the hundreds are the same. Move on to the tens: 340 has 4 tens and 390 has 9 tens. 9 tens is more than 4 tens, so 390 is larger than 340. The ones are never needed.
340: 3 hundreds and 4 tens.
390: the same 3 hundreds, and 9 tens. The tens are the first place that differs, and 9 tens is more.
start at the left
Compare the places from the left until one differs
352 and 348 have the same hundreds, so the tens decide: 5 tens is more than 4, and 352 is larger. The ones are never reached, even though 8 is more than 2.
Why the left decides
The place on the left is worth the most. Each place holds a digit from 0 to 9, so the tens and ones together can make at most 99, which is less than one more hundred. In the same way, the ones can make at most 9, which is less than one more ten. That is why the comparing starts on the left, and why the ones are looked at last.
The usual mistake is to start on the right. 253 and 235 have the same hundreds. Looking at the ones first, 5 is more than 3, and it looks as if 235 wins. But the tens come before the ones: 5 tens is more than 3 tens, so 253 is the larger number.
Putting numbers in order
To put numbers in order from smallest to largest, find the smallest first. 87 has only two digits, so it comes first. 340 and 390 both have three digits, and the tens show that 340 is smaller. So the order is 87, 340, 390.
On a number line the numbers sit in the same order, from left to right. Smaller numbers are further left, and larger numbers are further right.
Smallest to largest, left to right: 87, 340, 390.
Worked example: Three Numbers Put in Order
Question Three children count their stickers. Amy has 253, Bala has 235 and Chen has 325. (a) Who has the most stickers? (b) Write the three numbers in order. Begin with the smallest.
1.Write the numbers one under another in a chart, so that the hundreds, the tens and the ones line up.
The three numbers are in a chart, so the hundreds, the tens and the ones line up. 2.Look at the hundreds first. 325 has 3 hundreds. The other two numbers have only 2 hundreds.
Look at the hundreds first. 325 has 3 hundreds. The other two have only 2 hundreds. 3.(a) 325 is the greatest number, so Chen has the most stickers.
(a) 325 is the greatest, so Chen has the most stickers. 4.253 and 235 have the same hundreds, so look at the tens. 5 tens is more than 3 tens, so 253 is greater than 235.
253 and 235 have the same hundreds, so look at the tens. 5 tens is more than 3 tens. 5.(b) In order from the smallest, the numbers are 235, 253, 325.
(b) From the smallest: 235, 253, 325.
Answer: (a) Chen, with 325 stickers; (b) 235, 253, 325
Common mistakes
- Looking at the ones first and saying that 235 is greater than 253 because 5 is more than 3. The ones are worth the least, so they are compared last.
- Writing the order as 325, 253, 235. The question says to begin with the smallest, so 235 comes first and 325 comes last.