Do you want to learn faster and more easily?

Then why not use our learning videos, and practice for school with learning games.

Rating

Be the first to give a rating!
The authors
Team Digital

## What Are Three-Digit Numbers? – Introduction

Three-digit numbers range from 100 to 999.

Three-digit numbers are never smaller than 100 and never greater than 999. Each number has three digits: one in the hundreds place, one in the tens place and one in the ones or units place.

Place value is crucial when working with three-digit numbers, as it informs us of a digit's value. Recognising the hundreds, tens and ones place is vital for performing calculations like addition of 3 digit numbers correctly. Let’s have a look at the number 367 in a place value chart. The digits are placed in the hundreds (H), tens (T) and ones place (O):

H T O
3 6 7

## Foundational Steps to Add Three-Digit Numbers

Once pupils understand three-digit numbers, they can begin learning how to add them. There are essential steps to simplify the process. Three-digit numbers can be difficult to add, so always use a place value chart or use a standard written method to add three-digit numbers. Look at the following steps on how to solve 3 digit addition.

Write down the numbers in a standard written format, aligning digits according to their place value.

Begin by adding the digits in the ones place. If the sum is a two-digit number, write down the digit in the ones place and carry over the ten to the tens place.

When calculating 3 digit column addition with carrying, it is important to understand what we are doing. Carrying over is a fundamental concept when the sum in the ones and tens place is a two-digit number. It involves adding the carried-over number to the sum of the digits in the next place.

3. Move on to adding tens

Once you added the unit digits, move on to adding the digits in the tens place. Do not forget to also add any numbers that you carried over from adding the unit digits. If the sum is a two-digit number, write down the unit and carry over the ten to the hundreds place.

4. Move on to adding hundreds

Once you added the digits in the tens place, move on to adding the digits in the hundreds place. Do not forget to also add any numbers that you carried over from adding the tens digits. If the sum is a two-digit number, write down the sum in the hundreds and thousands place.

## Step-by-Step Guide to Three-digit Addition with Carrying Over

Let’s look at the example equation and do it together, step by step. Let’s complete 391 + 139.

Write down the first number 391, and right underneath it 139, in a standard written format. Align digits according to their place value - make sure that 9 is under 1, 3 under 9 and 1 under 3. See the example below:

Begin by adding the digits in the ones place. In this case, we will add 9 and 1. As you know, the sum of these two digits is 10. This means that you will have to write down 0 in the ones place and carry 1 ten over.

Carrying over is a fundamental concept when the sum in the ones and tens place is a two-digit number. It involves adding the carried-over number to the sum of the digits in the next place.

3. Move on to adding tens

Once you have added the unit digits, move on to adding the digits in the tens place. Here we will need to add 3 tens and 9 tens. However, let’s not forget that there is one more ten that we carried over from the units place. In this case, 3 plus 9 plus 1 equals 13. As this sum is over 10, we will have to carry over again. See the example below:

4. Move on to adding hundreds

Once you have added the digits in the tens place, move on to adding the digits in the hundreds place. Here we add 1 hundred and 3 hundred, their sum equals 4 hundred. But do not forget to also add the 1 hundred we carried over from the tens column! Write the digit 5 in the hundreds place. Well done, you have added two three-digit numbers and their sum is 530 - five hundred and thirty. Look at the representation below:

## Adding Three-Digit Numbers – Common Mistakes

Common errors include forgetting to carry over or carrying over incorrect values. Also, pay attention to zeros in the ones or tens place. It is important to never skip them and always remember to keep them as place value holders. Practice and attention to detail can help avoid these mistakes.

## Adding Three-Digit Numbers – Conclusion

Mastering the addition of three-digit numbers is essential for students, as it lays the groundwork for more advanced mathematical concepts and applications. With understanding, practice and the use of available resources, students can efficiently and accurately add three-digit numbers. Consistent practice and engagement with various learning tools and materials will facilitate mastery of this fundamental skill.

The key steps to successful three-digit addition are:

Step # What to do
3 Move on to adding tens
4 Move on to adding hundreds

For further 3-digit addition practice, have a look at our addition 3-digit numbers worksheets featuring 3-digit addition word problems. We also have 3 digit addition interactive exercises, 3 digit addition games and 3 digit addition story problems.

How to teach 3 digit addition with regrouping: what is 3 digit addition with regrouping?
Why is understanding ‘carrying over’ important?
Can three-digit addition be done mentally? How?
How to check if the addition of three-digit numbers is correct when solving 3 digit addition problems?
What if there are more than two numbers to add?
How is subtraction of three-digit numbers related to addition?

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Adding 3-Digit Numbers.
• ### What is the place value of the underlined digit?

Hints

Put your number in the columns below.

Is the underlined digit in the hundreds, tens or ones column?

Solution

If your number has 3 digits it will have a hundreds, tens and ones number.

306 Tens

3 hundreds 0 tens 6 ones

271 Hundreds

2 hundreds 7 tens 1 one

981 Ones

9 hundreds 8 tens 1 one

• ### Can you identify the mistake?

Hints

Ensure the numbers have been placed in the correct column.

As the answer from the tens column is more than 2 digits, we need to carry the tens number over to the hundreds column.

Solution

Check each column. Have the numbers been added correctly?

5 + 3 = 8

If you add the column and the answer is greater than 10, you must carry across.

4 + 7 = 11

We need to carry across the tens number of 11 to the hundreds column.

• ### Work out the answer to the calculation by placing the digits into the correct boxes.

Hints

Ensure you have put all of the numbers for the calculation in the correct place.

Don't forget, if your answer in the ones or tens column is greater than 9, you need to carry the tens digit of the number across to the next column.

Solution

Once the digits are in the correct column:

• Add up the ones column first. 4 + 3 = 7.
• Then your tens column. 4 + 6 = 10. We need to carry across the 1 to the hundreds column.
• Finally, your hundreds column. 1 + 3 + 2 = 6.

• ### Solve the problems using the column method.

Hints

Finally, hundreds.

Solution

473 + 326 = 799

306 + 291 = 597

651 + 367 = 1018

• ### What's the solution?

Hints

Add the digits in the ones column first.

3 + 5 =

Add the digits in the tens column next.

4 + 2 =

Solution

Add the digits in the ones column first 3 + 5 = 8

Then add the digits in the tens column 4 + 2 = 6

Finally, add the digits in the hundreds column 2 + 1 = 3

243 + 125 = 368

• ### Solve the answers to the problems.

Hints

Set your calculation out into the grid method. Making sure all digits are in the correct column.

Solution

Set your calculation out using the grid method shown in the video.

Add the digits in each column. Make sure you add them up in the correct order.

Ones: 2 + 4 = 6

Tens: 6 + 4 = 10 We need to carry across the 1 to the hundreds column

Hundreds: 1 + 3 + 2 = 6