A three-digit number is built from three places: hundreds, tens, and ones.
For example, 365 means three 100s, six 10s, and five 1s, the same as 300 plus 60 plus 5.
Apartment numbers and page numbers often go past 100; the same digit is worth a different amount depending on where it sits, and that is what place value means.
Change the number with the slider, look at how many blocks sit in the hundreds, tens, and ones columns, and compare two numbers by the length of their bars.
Numbers bigger than 100
A digit is not worth the same amount in every slot. Put 3 in the hundreds slot and it is 300; put that same 3 in the ones slot and it is just 3. When you write a three-digit number, the left slot is hundreds, the middle is tens, and the right is ones, so you can split the number into how many 100s, 10s, and 1s you gathered. You need that split first, because later when you compare two numbers you are not asking which digit looks bigger. You are asking which slot is carrying more.
🏠 Apartment numbers have three digits too
①Apartment numbers like 301 and 502 are three-digit numbers
②You can break a number into how many 100s, 10s, and 1s it has
③Once you know how many of each, big numbers are easy to read
Place-value blocks
365
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A three-digit number split into hundreds, tens, and ones blocks
At the top of the first picture is the three-digit number you picked with the slider, and below it are three columns for hundreds, tens, and ones. The left column has one gold square marked 100 for each hundred, the middle column has one blue bar for each ten, and the right column has one green dot for each one. The line at the bottom shows that hundreds × 100 + tens × 10 + ones × 1 equals the number at the top. The second picture shows the two numbers as horizontal bars scaled so that 999 would fill the full length, with the two numbers and >, <, or = written underneath.
💡 What is place value?
①The number of gold 100 squares in the left column is the hundreds digit
②Each blue bar in the middle stands for 10, and the number of bars is the tens digit
③Each green dot on the right stands for 1, and the number of dots is the ones digit
④Add the values of the three columns, as in the bottom line, and you get the number at the top
Comparing numbers
It is easy to pick the number that shows a 9 in the ones place and call that the larger one. Size for a three-digit number starts at the left slot, and if the hundreds digits differ that side is already larger. You only look at the tens when the hundreds match, and only then at the ones. A 9 in the ones slot is just 9; a 4 in the other number's hundreds slot is 400. How big the written digit looks and how much that slot is worth are not the same question.
425
398
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Comparing two three-digit numbers with bars
⚖️ How to compare
①Compare the hundreds first
②If the hundreds are the same, compare the tens
③If the tens are the same too, compare the ones
④398 has a 9 in it, but 425 is bigger because its hundreds digit is bigger
Wrap-up
Building a three-digit number
hundreds × 100 + tens × 10 + ones × 1
Multiply each digit by its place value and add them up
The range of three-digit numbers
100 to 999 (smallest: 100, largest: 999)
Three-digit numbers go from 100 to 999
🎯 Remember
①Three-digit numbers go from 100 to 999
②Of the three places, the hundreds place has the greatest value
③Compare numbers starting from the highest place
④The same digit stands for a different value in a different place
⑤In 365, the 3 is in the hundreds place, the 6 in the tens place, and the 5 in the ones place
Examples and unit check
Example 1
What three-digit number has 4 in the hundreds place, 7 in the tens place, and 2 in the ones place?
1
Find the value of each place: 4×100 = 400, 7×10 = 70, 2×1 = 2.
2
Add them: 400 + 70 + 2 = 472.
▸ 472
A three-digit number = (hundreds)×100 + (tens)×10 + (ones)×1.
Example 2
Which is bigger, 583 or 561?
1
Start from the highest place. Both hundreds digits are 5.