ACARA v9 CONTENT DESCRIPTION “apply knowledge of place value to add and subtract decimals, using digital tools where appropriate; use estimation and rounding to check the reasonableness of answers”
Builds on: Comparing and Ordering Fractions (AC9M6N03). Fractions and decimals are two ways of naming the same values — here that idea extends to adding and subtracting decimals using place value.
Decimal place value
Adding and subtracting decimals rests on understanding place value. Just as the digits to the left of the decimal point are ones, tens and hundreds, the digits to the right are tenths, hundredths and thousandths, each place worth a tenth of the one before it. In 3.45 the 3 is three ones, the 4 is four tenths, and the 5 is five hundredths. Knowing exactly what each digit is worth is what makes calculating with decimals possible, because every operation works place by place, matching tenths with tenths and hundredths with hundredths.
Decimal place value
Each place after the decimal point is worth a tenth of the place before it.
In 3.45, each digit's place tells its value — tenths are worth ten times a hundredth, just as ones are ten times a tenth.
Lining up to add
The golden rule for adding or subtracting decimals is to line up the decimal points. When the points are aligned, every place sits above its match: ones under ones, tenths under tenths, hundredths under hundredths. Then you add or subtract each column just as with whole numbers. Writing in extra zeros so both numbers have the same number of decimal places, like 1.2 as 1.20, can make the alignment clearer. Misaligning the points is the most common mistake, so lining them up carefully is the single most important habit in decimal arithmetic.
Lining up to add
To add decimals, line up the decimal points so each place adds to its match.
Line up the points, then press to add.
Adding decimals
To add decimals, line up the points and add each place from right to left, carrying to the next place whenever a column reaches ten, exactly as with whole numbers. Adding 1.5 and 2.3, the tenths 5 and 3 make 8 tenths and the ones 1 and 2 make 3, giving 3.8. When a column of tenths reaches ten or more, as in 0.45 + 0.55, the extra ten tenths carry over as one whole, giving 1.00. The decimal point in the answer stays in line with the points above it, so the places never drift.
Adding decimals
Add the matching places, carrying to the next place when a column reaches ten.
What is 1.5 + 2.3? Pick A, B or C.
Subtracting decimals
Subtracting decimals follows the same alignment rule. Line up the points and subtract each place from right to left, borrowing from the next place when the top digit is too small, just as with whole numbers. For 3.8 minus 1.5, the tenths 5 from 8 leave 3 and the ones 1 from 3 leave 2, giving 2.3. When subtracting from a number like 5.0, writing it as 5.0 and borrowing across the places keeps the arithmetic clear. Keeping the decimal points aligned ensures each digit is taken from its correct place.
Subtracting decimals
Line up the points and subtract each place, borrowing from the next place when needed.
What is 3.8 − 1.5? Pick A, B or C.
Estimating with rounding
Before calculating exactly, it is wise to estimate, and rounding each decimal to the nearest whole number gives a fast estimate. For 4.8 + 3.1, rounding to 5 + 3 suggests the answer is about 8. This rough figure is not the exact answer but a sensible ballpark to aim for. Estimating first, then calculating, then comparing the two is a powerful habit: rounding gives the expected size, and the exact calculation fills in the detail. Digital tools can do the exact arithmetic, but the estimate is what tells you to trust the result.
Estimating with rounding
Rounding each decimal to a whole number gives a quick estimate to check your answer against.
Press to estimate by rounding each number first.
Checking reasonableness
An estimate earns its keep by checking whether an exact answer is reasonable. If rounding says 4.8 + 3.1 should be about 8, then an exact answer of 7.9 is reasonable, while answers like 79 or 0.79 are plainly wrong, signalling a misplaced decimal point. Comparing a result against a quick estimate catches the large errors that matter most, especially the slips in decimal placement that change an answer by a factor of ten. Checking reasonableness turns calculation from a leap of faith into a result you can defend.
Checking reasonableness
A rounded estimate tells you whether the exact answer is sensible or a mistake.
Use the estimate to judge the answer. Pick A, B or C.
Where decimals lead
Adding and subtracting decimals is the everyday mathematics of money, measurement and data, from totalling a shopping bill to combining lengths and masses. The place-value thinking behind it, and the habit of estimating to check, carry forward into multiplying and dividing decimals, into percentages, and into every later use of measurement and money. Calculating accurately with decimals while always sense-checking the result is a practical skill that students will rely on throughout school and well beyond it.
Quick self-check
1. In the number 3.45, the digit 4 is in the...
2. When adding decimals, you should first...
3. What is 1.5 + 2.3?
4. What is 3.8 − 1.5?
5. Rounding to check, 4.8 + 3.1 is about 5 + 3 = 8. Which exact answer is reasonable?