## Adding numbers

When we add numbers, place value is important. When we work through a problem such as $456+349$456+349, we have to start at the right hand side, and work to the left. Adding whole numbers with three digits is an ideal way to move to adding decimals to three decimal places. You may like to refresh your memory of adding numbers with one decimal place, before tackling numbers with three decimal places.

## With decimals in our numbers

Having decimals in our numbers doesn't require us to do anything different, it's just that the value of our digits changes.

Imagine if, now, we have $0.456+0.349$0.456+0.349. While the digits are the same, the value of the numbers are different. Here, instead of adding $456$456 to $349$349, we are adding $456$456 hundredths to $349$349 hundredths. Our answer is $805$805 hundredths, which is less than $1$1. So, while the digits are the same, the answer is $1000$1000 times smaller! In our first video, we look at adding numbers with decimals to three places.

Remember!

When we add decimals, we always start with the smallest value, which is the number furthest to the right.

## Renaming

In the second video, you can see an example of adding two numbers with decimals but this time we need to regroup, or rename, some decimals. We use the same process that we use for whole numbers. Once again, we just have more steps to work through.

## Adding decimals with no place-value table

Finally, in our third video, we work through an example without the place value table! Hopefully, you have seen how it helps and now feel confident to try this yourself. It's the same process, but we need to be careful with how we write our answers so that our numbers line up in the correct places.

Oh, and we will also look at how to regroup from decimals to whole numbers. You'll soon see it's the same process we always use, we just have to keep moving left.

Remember!

It's also important to line up the place value columns. Estimating our answer is a great way to check that our decimal point is in the correct spot.

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#### Worked examples

##### Question 1

Find $1.007+0.1$1.007+0.1 giving your answer as a decimal.

##### Question 2

Find $3.003+2.007$3.003+2.007 giving your answer as a decimal.

##### Question 3

Find $2.066+6.025$2.066+6.025 giving your answer as a decimal.