Table of Contents
What is Place Value?
Place value is the value of each digit in a given number.
Let us understand this by considering the number 123.
In this number, the place value of digit 3 is 3 ones, or 3. The place value of digit 2 is 2 tens, or 20, and the place value of 1 is 1 hundred, or 100.
It can be represented with the help of a cube diagram, where each cube represents the number 1. This makes the value of ten such cubes equal to 10 and a hundred such cubes equal to 100.
Each place in a number can have any digit from 0 to 9. However, for two-digit numbers, three-digit numbers, and so on, the first digit cannot be 0.
For example:
In a three-digit number, the ones place can have the values 0, 1, 2, 3, and so on, till 9. The tens place also follows this. However, the hundreds place cannot have 0. Except 0, there can be any other digit such as 1, 2, 3, and so on.
For example:
324, 345, 432, and 869 are all three-digit numbers.
098, 076, and 006 are not three-digit numbers.
Also, each place can have only one digit in a given number.
In the above diagrams, it is illustrated that:
10 ones = 1 tens
10 tens = 1 hundreds
This is important to learn because it is applied to the addition of numbers. Suppose two numbers are added, and if the ones digits of these numbers sum up to more than 9, we carry forward to the tens digit. Similarly, if the tens digit are added and if they exceed 9, it is carried forward to the hundreds place.
Regrouping
There are several methods for adding two numbers. One such method is addition by regrouping. As the name suggests, in this method, ten ones are regrouped to form one ten and zero ones, ten tens are regrouped to form one hundred and zero tens, and so on.
For example, if we have two numbers, 159 and 542, the addition of these numbers using regrouping can be shown as follows:
In the above sum, the digits in the ones place are regrouped to get 1 ten and 1 one. The 1 ten is then carried over to the tens digits. Now, the digits in the tens place are again regrouped to form 1 hundred. This hundred is then carried over to the hundreds place. Finally, the digits in the hundreds place are added together. Again, to perform regrouping, we must keep in mind the following points:
- 10 ones make 1 tens and the resulting tens are shifted to the tens column.
- Similarly, 10 tens make 1 hundred and the resulting hundreds are shifted to the hundreds column.
This can also be seen below:
Helpful Resources for Kids
Revise Math formulas and important concepts using our Math worksheets! These worksheets help students to develop Math skills in a fun and interesting way. Click the link below to get all the easy-to-comprehend math calculators and worksheets.
Solved Examples
Question 1:
Lucas has 109 bananas in his basket and James has 312 more than him. How many bananas does James have?
Solution:
Lucas has 109 bananas in his basket.
James has 312 more bananas than Lucas. Let us add 109 to 312 using regrouping. As we can see, the digits in the ones place are regrouped to form 1 ten and 1 one. The 1 ten is then carried over to the tens digits. The rest of the addition does not require regrouping.
So, James has 421 bananas.
Question 2:
Stacy and Sarah are collecting pebbles. Stacy collects 527 pebbles and her friend Sarah collects 1048. How many pebbles do both of them collect together?
Solution:
The total number of pebbles can be found as:
When we add 1048 and 527, we will have to regroup the ones place to 1 ten and 5 ones. The ten is then carried over to the tens place. The rest of the addition does not require regrouping.
Therefore, Stacy and Sarah have 1575 pebbles in total.
Math Curriculum for all Grades
Our online math classes are specially designed keeping in mind your child’s age and academic level needs. Click the links below to know more details regarding our grades 1 to 8 online math classes.
The different strategies used for addition are :
- Adding on an open number line
- Compensation
- Partial sums
- Using models
- Regrouping
The different strategies used for subtraction are:
- Subtracting on an open number line
- Compensation
- Using models
- Regrouping