This Year 4 fractions and decimals lesson is written for pupils aged 8-9 and follows the National Curriculum. In short, it shows you how to link tenths and hundredths to decimals, order decimals and round decimals to the nearest whole number. Before you start, it helps to revise times tables to 12 x 12 and short multiplication and division, because this lesson builds on them.
Year 4 fractions and decimals lesson: what you will learn
Hello, I am Otto! Fractions and decimals are two ways of writing the same parts of a whole. You already know halves and quarters. In this chapter you learn about tenths and hundredths, how they are written with a decimal point, how to compare them and how they appear in money and measures.
Starter activity
A chocolate bar has 10 equal pieces. Ella eats 3 pieces. She has eaten 3 out of 10 pieces. We write this as the fraction 3⁄10 and as the decimal 0.3. A pound coin can also be split: 100 pennies make £1, so one penny is one hundredth of a pound, written 1⁄100 or £0.01. Fractions and decimals are everywhere!
Tenths
Definition: tenth
A tenth is one of ten equal parts of a whole. We write it as the fraction 1⁄10 or as the decimal 0.1. The dot in a decimal is called the decimal point. The digit just after the decimal point is the number of tenths.
The bar is split into 10 equal parts and 3 are shaded. The shaded part is 3⁄10 = 0.3.
Key fact: tenths as fractions and decimals
- 1⁄10 = 0.1, 2⁄10 = 0.2, 3⁄10 = 0.3 and so on up to 9⁄10 = 0.9.
- 10⁄10 = 1 whole. 15⁄10 = 1.5, which is one whole and 5 tenths.
- Dividing by 10: 7 ÷ 10 = 0.7 and 23 ÷ 10 = 2.3.
Hundredths
Definition: hundredth
A hundredth is one of 100 equal parts of a whole. We write it as the fraction 1⁄100 or as the decimal 0.01. The second digit after the decimal point is the number of hundredths.
There are 100 small squares and 37 are shaded. So 37⁄100 of the square is shaded. As a decimal this is 0.37. It is made of 3 tenths and 7 hundredths.
Rule: dividing by 100
To divide a whole number by 100, move each digit two places to the right of the decimal point. For example 45 ÷ 100 = 0.45, 7 ÷ 100 = 0.07 and 253 ÷ 100 = 2.53.
Example 1
Write 6⁄100 and 60⁄100 as decimals. Are they equal?
6⁄100 = 0.06 (0 tenths and 6 hundredths). 60⁄100 = 0.60, which is 6 tenths, the same as 0.6. They are not equal: 0.06 is much smaller than 0.6.
Place value with decimals
Place value now continues to the right of the decimal point. Each column is ten times smaller than the column on its left. After the ones comes the tenths column, then the hundredths column.
| Ones | . | Tenths | Hundredths |
|---|---|---|---|
| 3 | . | 4 | 7 |
In 3.47 the digit 3 is worth 3 ones, the 4 is worth 4 tenths (0.4) and the 7 is worth 7 hundredths (0.07). So 3.47 = 3 + 0.4 + 0.07.
Method: partitioning a decimal
- Write the whole number part and the decimal part separately.
- Say the value of each digit: ones, tenths, hundredths.
- Add the values together to check: 5.28 = 5 + 0.2 + 0.08.
Example 2
Partition 8.05 and say the value of each digit.
8.05 = 8 + 0.0 + 0.05. The 8 is worth 8 ones. The 0 in the tenths column is worth 0 tenths (it is a place holder). The 5 is worth 5 hundredths, 0.05. So 8.05 = 8 + 0.05.
Equivalent fractions and decimals
Key fact: tenths and hundredths
- One tenth is the same as ten hundredths: 1⁄10 = 10⁄100.
- So 3⁄10 = 30⁄100 and 0.3 = 0.30.
- Writing an extra zero at the end of a decimal does not change its value: 0.5 = 0.50.
Example 3
Write 7⁄10 as hundredths and as a decimal.
Multiply the top and the bottom by 10: 7⁄10 = 70⁄100. As a decimal, 7⁄10 = 0.7, and 70⁄100 = 0.70, which is the same.
Comparing and ordering decimals
Method: comparing decimals
- Write the numbers one under the other with the decimal points lined up.
- Compare the whole number parts first. The bigger whole number is the bigger decimal.
- If the whole numbers are equal, compare the tenths, and then the hundredths.
- Add zeros if it helps, so that every number has the same number of decimal places: 0.5 becomes 0.50.
Example 4
Put 0.6, 0.06, 0.65 and 0.5 in order, smallest first.
Write them all with two decimal places: 0.60, 0.06, 0.65 and 0.50. Compare tenths: 0.06 has 0 tenths (smallest); 0.50 has 5 tenths; 0.60 and 0.65 have 6 tenths and 65 is more than 60. Order: 0.06, 0.5, 0.6, 0.65.
Watch out
Longer does not mean bigger with decimals! 0.35 is bigger than 0.3, but 0.35 is smaller than 0.4 even though 0.35 has more digits. Compare 0.35 and 0.40: 35 hundredths is less than 40 hundredths.
Rounding decimals
Rule: rounding to the nearest whole number
Look at the tenths digit. If it is 5 or more, round up to the next whole number. If it is 4 or less, keep the whole number part and drop the decimal part. So 3.4 rounds to 3, 3.5 rounds to 4 and 3.78 rounds to 4.
Example 5
Round 7.46, 2.5 and 9.09 to the nearest whole number.
7.46: the tenths digit is 4, so round down to 7. 2.5: the tenths digit is 5, so round up to 3. 9.09: the tenths digit is 0, so round down to 9.
Decimals in money and measures
Money is the most common use of decimals. £3.45 means 3 pounds and 45 pence, which is 3 + 0.4 + 0.05 pounds. Measures also use decimals: 1.5 m means 1 metre and 5 tenths of a metre (50 cm), and 2.25 kg means 2 kg and 250 g. Always keep two decimal places for money, so write £4.50 and not £4.5.
Example 6
A ribbon is 2.7 m long. How many centimetres is that?
1 m = 100 cm, so 0.1 m = 10 cm. 2.7 m = 2 m + 7 tenths of a metre = 200 cm + 70 cm = 270 cm.
Did you know?
The decimal point was first used in Europe about 400 years ago. In some countries, such as France and Germany, people write a comma instead of a point, so they write 3,5 for three and a half. In the UK we use the point and in a calculator display you also see a point.
Otto's tip
To compare decimals, give every number the same number of decimal places by adding zeros at the end. Then you can compare them like whole numbers: 0.5 = 0.50, so 0.5 is more than 0.45 because 50 is more than 45!
How to use this Year 4 fractions and decimals lesson
First, read the key points so that you know where the Year 4 fractions and decimals lesson is going. Then work through each definition and worked example, and cover the solution before you read it. After that, practise with the fractions and decimals: tenths and hundredths worksheet and check every question with the worksheet answers. When you feel ready, test yourself with the multiple choice questions or the quick quiz. Finally, sit the fractions and decimals: tenths and hundredths test and mark it with the test answers.
Also, the starters are a good warm-up, so you can keep the key facts fresh. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday. In short, this Year 4 fractions and decimals lesson gives you everything you need for the chapter.
Similar pages
WorksheetFractions and decimals: tenths and hundredths – Year 4 maths worksheet with answers to download as PDF
AnswersFractions and decimals: tenths and hundredths – Year 4 maths worksheet answers to download as PDF
Multiple choice questionsFractions and decimals: tenths and hundredths – Year 4 maths multiple choice questions to download as PDF
QuizFractions and decimals: tenths and hundredths – Year 4 maths quiz to download as PDF
TestFractions and decimals: tenths and hundredths – Year 4 maths test to download as PDF
Test answersFractions and decimals: tenths and hundredths – Year 4 maths test answers to download as PDF
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