# Multiply numbers with thousandths by single digit numbers

Lesson

## Same but different

Have you noticed that each time we extend our decimal number, nothing really changes in how we solve problems? Just like with whole numbers, it's just the scale or size of the number that changes.

Multiplying numbers that include tenths or hundredths means part of the number is smaller than one. Multiplying a number that contains thousandths means we are multiplying by a number that contains parts much smaller than one. In the first video, we compare the size of a thousandth to hundredths and tenths and then multiply a number containing thousandths.

In our second video, we look at solving our problem vertically and using a couple of simple methods to check our answers seem reasonable. While this doesn't always tell us our answer is correct, it can definitely help us check our decimal place is in the correct spot.

Remember!

When we multiply by thousandths, we use the same process, but we have digits that have a smaller place value.

We can also use an approximation to check our answer, which helps make sure our decimal point is in the correct place.

#### Worked examples

##### Question 1

Use the area model to find $0.003\times6$0.003×6.

1. Fill in the area of the rectangle.

 $0.003$0.003 $6$6 $\editable{}$

##### Question 2

Use the area model to find $0.059\times5$0.059×5.

1. Fill in the areas of each rectangle.

 $0.05$0.05 $0.009$0.009 $5$5 $\editable{}$ $\editable{}$
2. What is the total area of the two rectangles, and therefore the answer to $5\times0.059$5×0.059?

##### Question 3

Use the area model to find $9.053\times7$9.053×7.

1. Fill in the areas of each rectangle.

 $9$9 $0.05$0.05 $0.003$0.003 $7$7 $\editable{}$ $\editable{}$ $\editable{}$
2. What is the total area of all three rectangles, and therefore the answer to $7\times9.053$7×9.053?