Multiply numbers with hundredths by single digit numbers
Multiplying decimals
When we multiply decimals, we can use of place value to help us. When our number had one decimal place, tenths, we saw how to multiply by thinking about our place value columns.
Decimals to two places
Suppose we have a number, such as $12.75$12.75, we can think of this as $12+0.75$12+0.75. Thinking about how numbers with decimals are constructed is something that can help us think about what we are actually doing when we are multiplying numbers with hundredth values.
When we multiply this by a whole number, we don't need to do anything new, just remember that our number is made up of hundredths, as well as whole numbers. Let's look at $12.75$12.75, using our place value columns.
| Tens | Units | . | Tenths | Hundredths |
|---|---|---|---|---|
| 1 | 2 | . | 7 | 5 |
In our first video, we're going to look at what the fraction $0.75$0.75 looks like, as well as what multiplying it by $4$4 might mean. At the end, we solve it mathematically and see that the answer is the same.
Ways to solve our problems
Now we can think of how to solve multiplication of decimals. One way is to use repeated addition, when we are multiplying by a small number. Another way is to partition our number. So, when working out $9.73\times5$9.73×5, we can work out $9\times5+0.7\times5+0.03\times5$9×5+0.7×5+0.03×5 and then add the answers together for our final solution.
The second video works through how to do this in detail, including some steps you may be able to work out in your head.
Solving vertically
You can also solve this as a vertical algorithm, as we did when working to tenths, by writing the problem out down your page. As always, estimating the answer is a great way to check your decimal place is in the correct spot. For example, when solving $15.25\times4$15.25×4, you could work out $15\times4=60$15×4=60. Then, this can help you work out where the decimal place should be in your final answer. Your answer would be larger than $60$60, so if you had an answer that was a bit larger than $6$6, you'd know your decimal place was not in the correct spot!
The way we solve these is no different to working with whole numbers, we just work on numbers that have a different place value.
Worked examples
Question 1
Find $0.08\times3$0.08×3, giving your answer as a decimal.
Question 2
Find $9\times1.29$9×1.29, giving your answer as a decimal.
Question 3
Find $8\times7.87$8×7.87, giving your answer as a decimal.