Year 5 Maths: Decimals on the Number Line

Introduction to Decimals

Hello, Year 5! Today, we are going to learn about decimals and how we can place them on a number line. Decimals are numbers that are not whole; they are parts of a whole. For example, 0.5 is half of 1, and 0.25 is a quarter of 1.

What is a Number Line?

A number line is a straight line that shows numbers in order. The numbers increase from left to right. We can use a number line to help us see where decimals fit in among whole numbers.

Example:

If we have a number line from 0 to 1, it looks like this:

 0         1 |---------| 

Now, between 0 and 1, we can place decimals.

Placing Decimals on the Number Line

Step 1: Identify the Whole Numbers

First, look for the whole numbers. In our example, the whole numbers are 0 and 1.

Step 2: Divide the Space Between Whole Numbers

We need to divide the space between the whole numbers into equal parts. For example, if we want to place 0.5, we divide the space between 0 and 1 into 2 parts:

 0         1 |----|----| 0.0  0.5  1.0 

Step 3: Place the Decimal

Now, we can see that 0.5 is right in the middle of 0 and 1.

Example with More Decimals:

Let’s try placing 0.25 and 0.75 on the same number line.

1. Divide the space between 0 and 1 into 4 parts since 0.25 is a quarter of 1:

 0         1 |---|---|---|---| 0.0 0.25 0.5 0.75 1.0 

2. Now, we can see where 0.25 is (the first mark) and where 0.75 is (the third mark).

Key Rules for Decimals on the Number Line

1. Whole Numbers: Whole numbers are at the ends of the number line.
2. Divisions: The space between whole numbers can be divided into tenths, hundredths, etc., depending on the decimals you are using.
3. Decimal Placement: Place the decimal at the correct division point.

Tips and Tricks

• Visualisation: Draw your number line to help you see where the decimals fit.
• Practice: The more you practice placing decimals, the easier it will become!
• Use Fractions: Sometimes, thinking of decimals as fractions can help. For example, 0.5 is the same as 1/2.

Questions

Easy Level Questions

1. What is 0.1 on the number line between 0 and 1?
2. Where does 0.3 fit on a number line between 0 and 1?
3. Place 0.4 on the number line.
4. Where would you find 0.8 on the number line?
5. Which decimal is closer to 0: 0.2 or 0.5?
6. Is 0.7 to the left or right of 0.5?
7. Place 0.6 on the number line.
8. Where does 0.0 belong on the number line?
9. What fraction is equal to 0.25?
10. How many tenths are there in 0.9?

Medium Level Questions

1. Divide the space between 0 and 1 into 5 parts. Where is 0.2?
2. Where would you place 0.15 on a number line from 0 to 1?
3. If you have 0.55, where does it go on the number line?
4. Is 0.3 closer to 0 or 1?
5. What is halfway between 0 and 1?
6. Place 0.85 on the number line.
7. How many parts do you need to divide to show 0.75?
8. Where is 0.6 compared to 0.5 on the number line?
9. If you have 0.01, where does it go on a number line from 0 to 1?
10. Which is larger: 0.4 or 0.5?

Hard Level Questions

1. Divide the space between 0 and 1 into 10 parts. Where is 0.07?
2. What is the position of 0.95 on the number line?
3. If you have 0.32, where would you place it?
4. How would you place 0.12 on a number line divided into 10 parts?
5. Where is 0.45 compared to 0.5 on the number line?
6. What decimal is halfway between 0.3 and 0.4?
7. If you have 0.99, where does it fit on the number line?
8. Where does 0.22 go on a number line divided into 100 parts?
9. How many hundredths are in 0.25?
10. If you have 0.77, is it closer to 0.7 or 0.8?

Answers to the Questions

Easy Level Answers

1. 0.1 is the first mark.
2. 0.3 is the third mark.
3. 0.4 is the fourth mark.
4. 0.8 is the eighth mark.
5. 0.2 is closer to 0.
6. 0.7 is to the right of 0.5.
7. 0.6 is the sixth mark.
8. 0.0 is at the start of the line.
9. 0.25 is the same as 1/4.
10. There are 9 tenths in 0.9.

Medium Level Answers

1. 0.2 is the second mark.
2. 0.15 is between 0.1 and 0.2.
3. 0.55 is the fifth mark after 0.5.
4. 0.3 is closer to 0.
5. Halfway is 0.5.
6. 0.85 is the eighth mark from 0.
7. You need to divide into 4 parts to show 0.75.
8. 0.6 is to the right of 0.5.
9. 0.01 is the first mark after 0.
10. 0.5 is larger than 0.4.

Hard Level Answers

1. 0.07 is the seventh mark if divided into 100 parts.
2. 0.95 is the ninth mark before 1.
3. 0.32 is the third mark after 0.3.
4. 0.12 is the second mark after 0.1.
5. 0.45 is slightly to the left of 0.5.
6. 0.35 is halfway.
7. 0.99 is almost at the end of the line, before 1.
8. 0.22 is the 22nd mark if divided into 100 parts.
9. There are 25 hundredths in 0.25.
10. 0.77 is closer to 0.8.

Great work today, Year 5! Keep practicing placing decimals on the number line, and soon it will be easy for you!