Extending multiplication to smaller numbers
We've already looked at how we can use our knowledge of place value and the ten times tables to multiply large numbers. For example, if we were asked to solve $5\times60$5×60, we could think $5\times60$5×60 is ten times bigger than $5\times6$5×6, so the answer will also be $10$10 times bigger. In other words:
| $5\times60$5×60 | $=$= | $5\times6\times10$5×6×10 |
| $=$= | $30\times10$30×10 | |
| $=$= | $300$300 |
We can also use a similar process to multiply small numbers (e.g. decimals). Let's look how.
Remember each column in the place value table is ten time bigger than the last. For example, $10$10 hundredths make $1$1 tenth, $10$10 tenths make $1$1 unit and so on.
Also, remember that if we divide a number by a power of ten (e.g. $10,100,1000$10,100,1000), the numbers will move down columns in the place value table.
So let's see what happens when we multiply decimals.
You can multiply decimals as whole numbers, then add in the decimal place. The number of decimal places in the answer will be the same as the number of decimal places in the question.
e.g. $0.3\times0.8=0.24$0.3×0.8=0.24 -There are $2$2 decimal places in the question and $2$2 in the answer.
Worked Examples
Question 1
Using your knowledge of place value, solve these related number facts.
$4\times12$4×12=
$0.4\times1.2$0.4×1.2=
Question 2
If $5\times15=75$5×15=75, what is $0.5\times15$0.5×15?
Question 3
Solve this multiplication using your knowledge of place value. Give your answer to $2$2 decimal places.
$0.04\times10$0.04×10