Number
Decimals
3rd Class · 4th Class · 5th Class · 6th Class
- ✓By the end of this lesson students will be able to identify and understand the place value of tenths, hundredths, and thousandths.
- ✓By the end of this lesson students will be able to convert simple fractions to decimals and vice versa.
- ✓By the end of this lesson students will be able to add and subtract decimal numbers accurately.
- ✓By the end of this lesson students will be able to multiply decimal numbers.
- ✓By the end of this lesson students will be able to divide decimal numbers by whole numbers and by other decimal numbers.
Key concepts
A decimal is a way of writing numbers that are not whole numbers. It uses a decimal point to separate the whole number part from the fractional part. For example, in 3.5, '3' is the whole number part and '.5' is the fractional part.
The decimal point is the dot that separates the whole number part of a number from its fractional part. Digits to the left of the decimal point are whole numbers (units, tens, hundreds, etc.), and digits to the right represent parts of a whole.
The first digit after the decimal point represents tenths. One tenth means one part out of ten equal parts of a whole. For example, 0.1 is one tenth, and 0.7 is seven tenths.
The second digit after the decimal point represents hundredths. One hundredth means one part out of one hundred equal parts of a whole. For example, 0.01 is one hundredth, and 0.25 is twenty-five hundredths.
The third digit after the decimal point represents thousandths. One thousandth means one part out of one thousand equal parts of a whole. For example, 0.001 is one thousandth, and 0.123 is one hundred and twenty-three thousandths.
To add decimals, you must line up the decimal points. This ensures that you are adding units to units, tenths to tenths, hundredths to hundredths, and so on. Then, add the numbers as you would with whole numbers, carrying over when necessary.
To subtract decimals, similar to addition, you must line up the decimal points. This ensures correct place value subtraction. You may need to add zeros to the end of a decimal number to make the number of decimal places equal before subtracting. Then, subtract as you would with whole numbers, borrowing when necessary.
To multiply decimals, first multiply the numbers as if they were whole numbers, ignoring the decimal points. Then, count the total number of decimal places in the original numbers (the factors). Place the decimal point in your answer (the product) so that it has the same total number of decimal places.
When dividing decimals, if the divisor (the number you are dividing by) is a decimal, you need to make it a whole number. Do this by moving the decimal point to the right until it is at the end of the number. You must then move the decimal point in the dividend (the number being divided) the same number of places to the right. After this, divide as you would with whole numbers, placing the decimal point in the quotient directly above the new decimal point in the dividend.
Key facts to remember
- 1The decimal point separates the whole number part from the fractional part of a number.
- 2The first digit after the decimal point is the tenths place (e.g., 0.1 = 1/10).
- 3The second digit after the decimal point is the hundredths place (e.g., 0.01 = 1/100).
- 4The third digit after the decimal point is the thousandths place (e.g., 0.001 = 1/1000).
- 5When adding or subtracting decimals, always line up the decimal points.
- 6When multiplying decimals, count the total number of decimal places in the numbers being multiplied to place the decimal point in the answer.
- 7When dividing by a decimal, move the decimal point in both the divisor and the dividend until the divisor is a whole number.
- 8Adding zeros to the end of a decimal number (e.g., 0.5 = 0.50 = 0.500) does not change its value.
Worked examples
Example 1
Calculate: 15.75 + 8.3 - 4.125
Answer
19.925
Always align the decimal points when adding or subtracting. Adding zeros to the end of a decimal does not change its value.
Example 2
Multiply: 6.25 × 3.4
Answer
21.250 or 21.25
Remember that 21.250 is the same as 21.25. You can drop trailing zeros after the decimal point if there are no other digits following them.
Example 3
Divide: 10.8 ÷ 0.45
Answer
24
The key to dividing by a decimal is to transform the problem into dividing by a whole number. Whatever you do to the divisor, you must do to the dividend.
Common mistakes
- ✗Not aligning the decimal points when adding or subtracting, leading to incorrect place value operations.
- ✗Incorrectly counting the total number of decimal places when multiplying, resulting in the decimal point being in the wrong position in the product.
- ✗Forgetting to move the decimal point in the dividend when making the divisor a whole number during division.
- ✗Confusing the place values, for example, thinking 0.1 is smaller than 0.05 because 1 is smaller than 5 (when 0.1 is 10 hundredths and 0.05 is 5 hundredths).
- ✗Ignoring the decimal point completely and treating all numbers as whole numbers throughout the calculation.
Exam tips
- ★Use squared paper for calculations involving decimals to help keep your digits and decimal points neatly aligned.
- ★Always estimate your answer before calculating. This helps you spot if your final answer is wildly incorrect (e.g., 2.1 × 3.9 should be roughly 2 × 4 = 8, not 80 or 0.8).
- ★Read the question carefully to understand what operation is required (+, −, ×, ÷) and what level of precision is needed for the answer (e.g., 'to two decimal places').
- ★After completing a calculation, quickly check your work, especially the placement of the decimal point.
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