Decimals

NZ Level 5

Further multiplication of numbers with decimals

Lesson

We've already learnt how to multiply by whole numbers. Now let's look at how to multiply by decimals.

Remember you can use all the strategies you already know to solve multiplication problems with decimals.

Tip

This is the way I like to solve problems with decimals- If you have a lot of decimal places is to pretend that the decimal point isn't there and do the multiplication as a whole number because we can expressed these values as the sum of their decimal parts (for example 12.1 can be expressed as 121 tenths). Then place the decimal point in the answer so that it has the same number of decimal places as the number being multiplied.

**Examples**

Sometimes we see questions with whole numbers and decimals.

**Evaluate:** $23.175\times3$23.175×3

**Think:** We could solve this as $23175\times3$23175×3, then count back $3$3 decimal places.

Remember that we can write $23.175\times3$23.175×3 like $\frac{23175}{1000}\times3$231751000×3. This is where the dividing by $1000$1000 (counting back $3$3 decimal places comes from).

**Do:**$23.175\times3=69.525$23.175×3=69.525

Got it? The same principles apply for when multiplying two decimals together.

**Evaluate: **$0.002\times0.4$0.002×0.4

**Think:**$2\times4=8$2×4=8 and there are $4$4 decimals places in the questions

**Do:**$0.002\times0.4=0.0008$0.002×0.4=0.0008

Evaluate $0.471\times5$0.471×5.

Evaluate $0.1\times0.1$0.1×0.1.

Evaluate $0.1\times0.007$0.1×0.007.

Understand operations on fractions, decimals, percentages, and integers