Primary 5 · Mathematics
P5 decimals
Once decimals start getting multiplied, the digits are rarely the problem. The decimal point is. The commonest slip drops a place and turns a small answer into one ten times too big. Here is the step where it happens.
- Level
- P5
- Usually taught
- Term 3
- Covers
- 3 concepts
What changes at P5
In Primary 5, decimals move from being read and ordered to being multiplied and divided. Your child works with tenths, hundredths and thousandths, and has to hold onto place value while the numbers get pushed around.
The arithmetic on the digits is usually fine. What costs marks is the decimal point: where it lands after a multiplication or division. That is a place-value decision, not a calculation.
The sentence that costs the mark
Work out 0.3 × 0.4.
What the working usually does
one place12=1.2
Multiplies 3 × 4 to get 12, then places the point one from the right, keeping a single decimal place.
What the question asked
two places12=0.12
Counts one decimal place in each factor, two in all, so the point goes two from the right.
The digits are 12 in both, so the working looks the same and correct right up to the last step. The only difference is how many decimal places the answer carries, and 0.3 × 0.4 has two. The size gives it away: 1.2 is bigger than either factor, which cannot happen when both are below 1.
The same question, worked properly
Multiply the digits
3 × 4 = 12Ignore the points for a moment and multiply as whole numbers. Three fours are twelve. The digits of the answer are always found this way first.
Count the decimal places in both factors
1 + 1 = 2 decimal placesThis is the step that fails. This is the step that decides the answer. 0.3 has one decimal place and 0.4 has one, so the answer has two. Placing only one gives 1.2, the wrong size.
Place the point two from the right
0.3 × 0.4 = 0.12Twelve becomes 0.12, which is twelve hundredths. Three tenths of four tenths is measured in hundredths, and that is why two places are needed.
Check the size
0.12 < 0.4Both factors are below 1, so the answer has to be smaller than either. 0.12 is smaller than 0.4, so it passes. 1.2 is bigger, so it fails on sight.
How can you tell it has clicked?
You do not need to multiply it yourself. Ask one question before the answer: is 0.3 × 0.4 bigger or smaller than 0.4? Smaller, because you are taking a fraction of it.
If your child agrees it must be smaller, then sees their answer is 1.2, they will catch their own mistake. The sense-check does the work that remembering the rule does not.
One thing to try tonight
Keep it to the size question. Three tenths of four tenths, is that bigger or smaller than four tenths? Smaller, so the answer has to be under 0.4.
That one question kills the 1.2 answer before any point-counting starts. It works for any decimal multiplication where both numbers are below one.
What your child will meet in this topic
- Multiplying Decimals
- Dividing Decimals
- Fractions and Decimals
Most Singapore schools introduce this in Term 3, though schools do differ by a term either way. If your child’s school runs a different order, you can set it in the schedule on your dashboard.
What it leads to
Placing the decimal point by place value is the same skill that runs through dividing decimals, converting between fractions and decimals, and every measurement question in P6. The point-counting habit carries all the way.
A child who sense-checks the size of a decimal answer rarely loses these marks. One who trusts the digits and forgets the point loses them quietly, a place at a time.
The same topic in other years
It comes back each year and gets harder, so it helps to see what came before and what is coming.
More in Primary 5
Other topics in the same year, so you can see what sits either side of this one.
Struggling with the working rather than the topic itself? How to help your child with problem sums
See how your child is doing on this topic
StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.