Decimals

NZ Level 5

Divide numbers with thousandths by a single digit number

Lesson

So far, we have divided decimals that have tenths and hundredths, by single digit numbers. This time, our decimals have thousandths. How can we approach these problems?

We need to do the same as we have done in earlier problems, but the scale of our number is different. We have a decimal that includes thousandths.

Imagine a swimming competition, where two swimmers appear to touch the wall at the same time. Often, the only way a winner can be decided is to look at their time in seconds, to the thousandths! So, a time of $13.356$13.356 seconds might help Joanne beat Emily, who swam a time of $13.359$13.359 seconds. This is where thousandths can be really useful.

Dividing a number with thousandths is no different, we just have more steps.

In the first video, we look at dividing or sharing, MAB blocks in our first example. Then, we look at calculating how fast you ran around an obstacle course. You only have your time for $3$3 laps, so will assume you ran each lap in the same time. By dividing your total time by $3$3, we can find out your time for 1 lap.

The next video is a very quick look at how we can solve the same problem, using short division. When you find you are more confident at dividing decimals, you can use short division to speed up the process. In this video, we already have our answer, so use this to help us work through short division. This is something you might like to do when you are practising. Perhaps you can calculate the answer first on a calculator, and then solve short division. If you get stuck along the way, you can see what each digit should be.

Finally, we look at a similar division example, but this time we need to rename, or regroup some of our digits. This is the same as when we divide whole numbers with regrouping, but the digits just have different values, depending on which place they are in.

The first video shows you how to do this using blocks, to physically see how we rename our digits, as well as short division. Short division is a great way to solve number problems such as this, but it can help to see the problem set out in more detail, so you will also find the same problem solved using long division at the end.

Did you know?

By solving the same problem using long division, you can see each step set out. This can often help develop your understanding of short division!

We want to find $4.844\div4$4.844÷4. We are going to do this by first partitioning the number.

Break up $4.844$4.844 into a sum of units, tenths, hundredths, and thousandths. Use whole numbers or decimals.

To find $4.844\div4$4.844÷4 we can divide each of $4$4, $0.8$0.8, $0.04$0.04, and $0.004$0.004 by $4$4 and add the results together.

Answer the following. Give each answer as a whole number or a decimal.

$4\div4=\editable{}$4÷4=

$0.8\div4=\editable{}$0.8÷4=

$0.04\div4=\editable{}$0.04÷4=

$0.004\div4=\editable{}$0.004÷4=

Hence, what is $4.844\div4$4.844÷4? Write your answer as a decimal.

We want to find $8.449\div7$8.449÷7

Choose the most reasonable estimate for $8.449\div7$8.449÷7

$0.01$0.01

A$1$1

B$0.1$0.1

C$10$10

D$0.01$0.01

A$1$1

B$0.1$0.1

C$10$10

DComplete the short division to find $8.449\div7$8.449÷7

$\editable{}$ $.$. $\editable{}$ $\editable{}$ $\editable{}$ $7$7 $8$8 $.$. $\editable{}$ $4$4 $4$4 $\editable{}$ $9$9

We want to find $18.158\div2$18.158÷2

Choose the most reasonable estimate for $18.158\div2$18.158÷2

$9$9

A$0.9$0.9

B$90$90

C$0.09$0.09

D$9$9

A$0.9$0.9

B$90$90

C$0.09$0.09

DComplete the short division to find $18.158\div2$18.158÷2

$\editable{}$ $.$. $\editable{}$ $\editable{}$ $\editable{}$ $2$2 $1$1 $8$8 $.$. $1$1 $\editable{}$ $5$5 $\editable{}$ $8$8

Understand operations on fractions, decimals, percentages, and integers