Number
Grade 2-3Decimals
Non-calculator decimal questions catch students out more through presentation than understanding, a decimal point in the wrong place turns a correct method into a wrong answer. This lesson covers adding, subtracting, multiplying and dividing decimals by hand, and converting between decimals and fractions.
What you need to know
- Line up the decimal points when adding or subtracting, filling gaps with zeros.
- To multiply decimals, ignore the points, multiply, then put back as many decimal places as both numbers had together.
- To divide by a decimal, multiply both numbers by 10 or 100 until the divisor is whole.
- A terminating decimal stops; a recurring decimal repeats a block forever.
Written by Asad, co-founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Adding and subtracting decimals
Line up the decimal points directly underneath each other before adding or subtracting, exactly as you would with whole numbers in columns. If one number has fewer decimal places, fill the empty spaces with zeros so every column lines up.
4.75 has two decimal places and 3.6 has one, so write 3.6 as 3.60 before adding, giving columns that line up cleanly.
Multiplying decimals
Ignore the decimal points and multiply the digits as whole numbers first. Then count the total number of decimal places in both original numbers, and place the decimal point that many places in from the right of the answer.
3.4 × 6: multiply 34 × 6 = 204. There was one decimal place in the question (in 3.4), so the answer has one decimal place: 20.4.
Dividing decimals
When dividing a decimal by a whole number, use short division as normal and keep the decimal point in the answer directly above the decimal point in the question.
8.4 ÷ 6: divide as 84 ÷ 6 = 14, then place the decimal point back in the same position, giving 1.4.
Converting between decimals and fractions
A decimal converts to a fraction using its place value as the denominator: the digits after the decimal point become the numerator, and the denominator is 10, 100 or 1000 depending on how many decimal places there are. Always simplify the resulting fraction fully.
A fraction converts to a decimal by dividing the numerator by the denominator. 3/4 becomes 0.75, because 3 ÷ 4 = 0.75.
Worked examples
Three exam-style questions, fully solved
Work out 3.6 + 4.75.
Easy- 1.Line up the decimal points, writing 3.6 as 3.60 so both numbers have two decimal places
- 2.Add as you would whole numbers in columns: 3.60 + 4.75
Answer: 8.35
Work out 8.4 ÷ 6.
Medium- 1.Ignore the decimal point and divide 84 ÷ 6 = 14
- 2.Place the decimal point back in the same position as in the original number
Answer: 1.4
Write 0.35 as a fraction in its simplest form.
Hard- 1.The digits after the decimal point are 35, and there are two decimal places, so the denominator is 100: 35/100
- 2.Find the highest common factor of 35 and 100, which is 5
- 3.Divide both the numerator and denominator by 5: 35 ÷ 5 = 7, 100 ÷ 5 = 20
Answer: 7/20
Practice
6 questions, marked instantly
Type an answer and check it. The worked solution appears once you have had a go. No login needed, and your progress saves in this browser.
Practice
Now try these yourself.
Type your answer and check it. The worked solution appears once you have had a go.
Work out 0.3 + 0.45
Work out 0.6 × 0.2
Work out 3 − 1.7
Work out 4.2 ÷ 0.6
Work out 0.05 × 1000
Work out 1.25 + 0.9 + 2
Avoid these
The mistakes students make most often
Not lining up the decimal points when adding or subtracting, especially when the numbers have a different number of decimal places.
Forgetting to place the decimal point back after multiplying two decimals as if they were whole numbers, or miscounting how many places to shift it.
Writing the decimal point in the wrong place in a division answer, instead of keeping it directly above where it was in the original number.
Using the wrong place-value denominator when converting a decimal to a fraction, for example writing 0.35 as 35/10 instead of 35/100.
Leaving a fraction converted from a decimal without simplifying it fully, for example stopping at 35/100 instead of 7/20.
FAQ
Questions students and parents ask
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What to learn next
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