Fractions, decimals & percentages
Decimals: Place Value, Operations and Rounding
Year 3 · Year 4 · Year 5 · Year 6
- ✓Identify the place value of digits in numbers with up to three decimal places.
- ✓Add and subtract decimals, ensuring correct alignment of decimal points.
- ✓Multiply decimals by whole numbers.
- ✓Round decimals to the nearest whole number or to a given number of decimal places.
Key concepts
The decimal point separates the whole number part from the fractional part of a number. Digits to the right of the decimal point represent parts of a whole. The first digit to the right is the tenths place (1/10), the second is the hundredths place (1/100), and the third is the thousandths place (1/1000). For example, in 3.456, '4' is in the tenths place, '5' is in the hundredths place, and '6' is in the thousandths place.
To add decimals, you must line up the decimal points vertically. This ensures that you are adding digits of the same place value (ones with ones, tenths with tenths, etc.). You can add zeros to the end of a decimal number to make sure all numbers have the same number of decimal places, which can help with alignment. Then, add the numbers as you would with whole numbers, carrying over when necessary, and place the decimal point in the answer directly below the other decimal points.
Similar to addition, when subtracting decimals, you must line up the decimal points vertically. Add zeros as placeholders if needed, especially if the top number has fewer decimal places than the bottom number. Then, subtract the numbers as you would with whole numbers, borrowing when necessary, and place the decimal point in the answer directly below the other decimal points.
To multiply a decimal by a whole number, first ignore the decimal point and multiply the numbers as if they were both whole numbers. Once you have your product, count the total number of decimal places in the original decimal number. Place the decimal point in your answer so that it has the same number of decimal places.
To round a decimal to a specific place value (e.g., nearest whole number, one decimal place), look at the digit immediately to the right of that place value. If this digit is 5 or more (5, 6, 7, 8, 9), you round up the digit in the target place value. If the digit is less than 5 (0, 1, 2, 3, 4), you keep the digit in the target place value the same. All digits to the right of the rounded place value are then dropped.
Key facts to remember
- 1The decimal point separates the whole number part from the fractional part of a number.
- 2Place values after the decimal point are tenths (0.1), hundredths (0.01), and thousandths (0.001).
- 3When adding or subtracting decimals, always line up the decimal points vertically.
- 4You can add zeros to the end of a decimal number without changing its value (e.g., 3.5 = 3.50 = 3.500).
- 5To multiply a decimal by a whole number, multiply as if they were whole numbers, then place the decimal point in the answer by counting the decimal places in the original decimal.
- 6To round a decimal, look at the digit to the right of the place you are rounding to. If it's 5 or more, round up; if it's less than 5, keep the digit the same.
Worked examples
Example 1
What is the value of the digit '7' in the number 4.72? Then, calculate 4.72 + 1.5.
Answer
The digit '7' represents 7 tenths (or 0.7). 4.72 + 1.5 = 6.22.
Always align the decimal points when adding or subtracting decimals. Adding zeros as placeholders can help.
Example 2
A baker uses 0.85 kg of flour for one cake. How much flour does he use for 3 cakes?
Answer
The baker uses 2.55 kg of flour for 3 cakes.
Remember to count the decimal places in the original number to correctly place the decimal point in your final answer.
Example 3
Round 15.38 to the nearest whole number and to one decimal place.
Answer
Rounded to the nearest whole number: 15. Rounded to one decimal place: 15.4.
Always identify the digit to the right of the place you are rounding to, as this digit determines whether you round up or keep the digit the same.
Common mistakes
- ✗Not lining up decimal points correctly when adding or subtracting, leading to incorrect place value addition/subtraction.
- ✗Incorrectly placing the decimal point in the final answer after multiplying decimals by whole numbers.
- ✗Rounding errors, especially with the '5' rule (e.g., rounding 3.45 down to 3.4 instead of up to 3.5).
- ✗Confusing place values, such as thinking 0.1 is smaller than 0.01, or misidentifying tenths, hundredths, or thousandths.
Exam tips
- ★Always show your working clearly, especially for column methods in addition and subtraction, to gain partial marks even if the final answer is incorrect.
- ★Read the question carefully to know exactly what place value you need to round to (e.g., nearest whole number, one decimal place, two decimal places).
- ★Estimate your answer before calculating to check if your final answer is reasonable. For example, 4.72 + 1.5 is roughly 5 + 2 = 7, so 6.22 is a reasonable answer.
- ★Use a ruler or grid paper to help keep numbers aligned in column calculations, which reduces errors.
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