Add & subtract decimals - Different decimal places
Theory
When decimals have different lengths, fill the empty places with zeros so the columns line up, then add or subtract as usual. A trailing zero does not change the value, and a whole number becomes \(5.00\).
When decimals have different numbers of places, fill the empty places with zeros so every column lines up.
A zero on the end of a decimal does not change its value: \(6.4 = 6.40\). It just gives the empty place a digit.
Fill each number to the same number of decimal places, then add or subtract as usual.
A whole number has no decimal part, so \(5\) becomes \(5.00\) when adding hundredths.
Add place-holding zeros so both numbers reach the same number of decimal places.
| Number | Written as | Why |
|---|---|---|
| \(6.4\) | \(6.40\) | fills the hundredths |
| \(9.2\) | \(9.20\) | fills the hundredths |
| \(5\) | \(5.00\) | a whole number needs a point |
How to add or subtract decimals of different lengths
- Line up the points. Write the numbers with the decimal points in a straight line.
- Fill the gaps. Put a zero in any empty place so both numbers match.
- Add or subtract. Work each column from the right, carrying or regrouping.
- Bring the point down. Place the decimal point straight down into the answer.
Write \(1.5\) as \(1.50\).
| \(1.50 + 2.25\) | \(=\) | \(3.75\) |
Write \(9.2\) as \(9.20\), then regroup.
| \(9.20 - 3.45\) | \(=\) | \(5.75\) |
Write \(5\) as \(5.00\).
| \(5.00 + 2.75\) | \(=\) | \(7.75\) |
There is \(0.75\) m left.
| \(1.50 - 0.75\) | \(=\) | \(0.75\) |
Common pitfalls
Frequently asked questions
How do you add decimals with different numbers of places?
Fill the shorter number with zeros so both have the same number of decimal places, then add column by column. For \(6.4 + 2.35\), use \(6.40 + 2.35 = 8.75\).
Does adding a zero to the end change a decimal?
No. \(6.4\) and \(6.40\) are equal. The extra zero only fills an empty place so the columns line up.
How do you subtract a decimal from a whole number?
Write the whole number with a decimal point and zeros, such as \(8\) as \(8.0\), then subtract with regrouping.
Why fill empty places with zeros?
So every place has a digit to add or subtract. Without the zero there is nothing in that column to work with.
What is \(5 + 2.75\)?
\(7.75\). Write \(5\) as \(5.00\), line up the points, then add: \(5.00 + 2.75 = 7.75\).