Key ideas
Place value
| Units | tenths | hundredths | thousandths |
|---|---|---|---|
| 3 | 4 | 7 | 2 |
In 3.472 the 4 is worth 4 tenths (0.4), the 7 is 7 hundredths (0.07) and the 2 is 2 thousandths (0.002).
Ordering
Line up the decimal points, fill gaps with zeros, then compare digit by digit from the left.
0.6 = 0.60 is bigger than 0.45.
Rounding
Look at the digit after the last one you keep: 5 or more rounds up.
3.476 to 2 decimal places is 3.48.
Adding and subtracting
Line up the decimal points. Fill any gaps with zeros, then add or subtract in columns.
× and ÷ by a whole number
Keep the decimal point in line. Use a chimney sum or a bus stop.
× and ÷ by 10, 100, 1000
× 10: digits move 1 place left. ÷ 10: 1 place right.
100: 2 places. 1000: 3 places.
× 30 = × 3, then × 10.
Place value
What is the value of the 5 in 12.358?(1 mark)
Use a place value table.
The 5 is in the hundredths column: 0.05✓1
| Tens | Units | tenths | hundredths | thousandths |
|---|---|---|---|---|
| 1 | 2 | 3 | 5 | 8 |
In plain EnglishThe first place after the point is tenths, then hundredths, then thousandths.
Ordering decimals
Put these in order, smallest first: 0.6, 0.45, 0.508, 0.06(1 mark)
Make them the same length.0.600, 0.450, 0.508, 0.0600.06, 0.45, 0.508, 0.6✓1
In plain EnglishFill with zeros so they all have 3 decimal places. Now compare them like whole numbers: 60, 450, 508, 600.
⚠ A common mistake: thinking 0.45 is bigger than 0.6 because 45 is bigger than 6. Line up the points first.
Rounding to decimal places
Round 7.2846 to 2 decimal places.(1 mark)
Look at the next digit.7.2846 3rd decimal place is 44 is less than 5, so 7.28✓1
In plain EnglishKeep 2 decimal places: 7.28. The next digit is 4, so we don't round up.
Adding decimals
Calculate 4.75 + 12.6(2 marks)
Line up the points.4.75 + 12.60 fill the gap with 0✓1
In plain English12.6 has one decimal place, so write it as 12.60 to match.
Add in columns.
= 17.35✓2
| 1 | |||||
| 1 | 2 | . | 6 | 0 | |
| + | 4 | . | 7 | 5 | |
| 1 | 7 | . | 3 | 5 |
In plain EnglishStart from the right. 7 + 6 = 13: write 3, carry the 1.
Subtracting decimals
Calculate 8.3 − 2.65(2 marks)
Line up the points.8.30 − 2.65✓1
In plain EnglishWrite 8.3 as 8.30 so both numbers have 2 decimal places.
Subtract in columns.
= 5.65✓2
| 78 | . | 123 | 100 | |
| − | 2 | . | 6 | 5 |
| 5 | . | 6 | 5 |
In plain EnglishYou can't take 5 from 0, so exchange: take 1 from the 3 to make the 0 into 10.
Multiplying by a whole number
Calculate 3.47 × 6(2 marks)
Multiply as if there were no point.347 × 6
347 × 6 = 2082✓1
| 2 | 4 | |||
| 3 | 4 | 7 | ||
| × | 6 | |||
| 2 | 0 | 8 | 2 |
In plain EnglishUse a chimney sum. The carries are shown in green.
Put the point back.3.47 has 2 decimal places: 20.82✓2
In plain EnglishEstimate to check: 3.5 × 6 = 21, so 20.82 is sensible.
Dividing by a whole number
Calculate 9.36 ÷ 4(2 marks)
Bus stop, keeping the point in line.
| 2 | . | 3 | 4 | |
| 4 | 9 | . | 13 | 16 |
In plain EnglishPut the decimal point in the answer directly above the point in 9.36.
Answer.9.36 ÷ 4 = 2.34✓2
In plain EnglishRead the answer from the top of the bus stop. Check: 4 × 2.34 = 9.36.
Multiplying and dividing by 10, 100 and 1000
Calculate 3.6 × 100(1 mark)
Move the digits 2 places left.3.6 × 100 = 360✓1
In plain EnglishMultiplying by 100 makes the number 100 times bigger: each digit moves 2 places to the left. Fill the empty units place with a zero.
Calculate 45 ÷ 1000(1 mark)
Move the digits 3 places right.45 ÷ 1000 = 0.045✓1
In plain EnglishDividing by 1000: each digit moves 3 places to the right.
Multiplying and dividing by multiples of 10, 100 and 1000
Calculate 2.3 × 40(2 marks)
Split the 40.× 40 = × 4, then × 10✓1
In plain English40 is 4 × 10, so multiply by 4 and then by 10.
Calculate.2.3 × 4 = 9.29.2 × 10 = 92✓2
In plain EnglishMultiply by 4 first, then multiply by 10 by moving the digits one place to the left.
Calculate 84 ÷ 200(2 marks)
Split the 200.÷ 200 = ÷ 2, then ÷ 100✓1
In plain English200 is 2 × 100, so divide by 2 and then by 100.
Calculate.84 ÷ 2 = 4242 ÷ 100 = 0.42✓2
In plain EnglishHalve 84 first, then divide by 100 by moving the digits two places to the right.
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Your turn
Non-calculator. Line up the decimal points, and type answers as decimals. For ordering, type the numbers separated by commas. Stuck? Tap Need a hint?