Primary 5 Decimals Study Guide
Primary 5 decimals in four short steps: moving digits by 10, 100 and 1000, then multiples such as 200, then changing units, then problems with two units. Each step has something to tap, with worked examples and a five-question check at the end.
Start here
What happens when you multiply a decimal by 10, 100 or 1000?
The digits move to new places; the decimal point stays still.
Each place is worth ten times the place on its right. Multiply by 10 and every digit moves one place to the left, so it is worth ten times as much. Divide by 10 and the digits move one place to the right. Your child uses these moves to change between units, and then in word problems that mix two units.
In this chapter, your child learns to:
- multiply and divide decimals by 10, 100 and 1000;
- multiply and divide by multiples such as 40 or 300;
- change km and m, m and cm, kg and g, L and ml, both ways;
- bring two units to one unit before calculating.
Step 1
Multiplying and dividing decimals by 10, 100 and 1000
Keep the point fixed; move the digits. To multiply by 10, move every digit one place left. By 100, two places left. By 1000, three places left. To divide, move the digits right by the same number of places. Write zeros as place holders where a place is empty, and a 0 before the point when the answer is less than 1.
Th thousands · H hundreds · T tens · O ones · t tenths · h hundredths · th thousandths
What is 26.5 ÷ 100?
Step 2
Multiplying and dividing decimals by multiples of 10, 100 and 1000
Split the multiple into two factors, and use both. 300 is 100 times 3, and 40 is 4 times 10. To divide by 300, divide by 100 first, then by 3. To multiply by 400, multiply by 4 first, then by 100. Split the decimal into parts when that makes the 1-digit step easier.
Tap Next step
Find 3.6 × 200.
Step 3
How to convert units with decimals
A smaller unit means more units; a larger unit means fewer. The length or mass stays the same; only the unit we count it in changes. There are 1000 m in 1 km, 100 cm in 1 m, 1000 g in 1 kg and 1000 ml in 1 L. Changing to a smaller unit, multiply, so the number gets bigger. Changing to a larger unit, divide, so the number gets smaller.
Tap Next step
Express 3.5 L in millilitres.
Step 4
Word problems with two units
Change the units first, then calculate. When one amount is in metres and another in centimetres, they are not the same kind of thing yet, so they cannot be added or subtracted. Convert one of them so both use the same unit. Then calculate, and give the answer in the unit the question asks for.
Tap Next step
Ravi has a ribbon 5 m long. He cuts off 6 pieces, each 45 cm long. How much ribbon is left, in metres?
Metres above, centimetres below. The conversion line makes them match.
A bag holds 2 kg of rice. Mrs Tan uses 3 cups of rice, 150 g each. How much rice is left, in kg?
Primary 5 decimals questions, worked step by stepHave a go on paper before you open anything. The hint nudges; each tap after that reveals one more line.
Find the value of 0.059 × 1000.
- The digits are 5 hundredths and 9 thousandths.
- Move each digit three places left: 5 goes to the tens, 9 to the ones.
- 0.059 × 1000 = 59.
Find the value of 6.3 ÷ 900 without using a calculator.
- 6.3 ÷ 900 = 6.3 ÷ 100 ÷ 9
- 6.3 ÷ 100 = 0.063
- 0.063 ÷ 9 = 0.007
Express 1.075 L in millilitres.
- 1 L = 1000 ml
- 1.075 L = (1.075 × 1000) ml
- = 1075 ml
A watermelon has a mass of 2.4 kg. A pineapple is 650 g lighter than the watermelon. What is the total mass of the two fruits? Give your answer in kilograms.
- 2.4 kg = 2.4 × 1000 = 2400 g
- pineapple = 2400 − 650 = 1750 g
- 1750 g = 1750 ÷ 1000 = 1.75 kg
- total = 2.4 + 1.75 = 4.15 kg
A tank has 12 L of water. Siti pours out 5 jugs of water, each holding 750 ml. Then she adds 1.8 L of water. How much water is in the tank now? Give your answer in litres.
- poured out = 5 × 750 = 3750 ml
- 3750 ml = 3750 ÷ 1000 = 3.75 L
- after pouring = 12 − 3.75 = 8.25 L
- now = 8.25 + 1.8 = 10.05 L
Step 5
Check yourself
Five short questions across the four steps. Nothing is saved, and each answer points to practice that fits.
1. What is 3.07 × 100?
2. Find 45 ÷ 500.
3. Express 2.06 m in centimetres.
4. Express 75 g in kilograms.
5. A jug holds 1.5 L of juice. 640 ml is poured out. How much juice is left, in millilitres?
Using this guide at home. Give your child a pencil and let them say each answer aloud before tapping. In Step 1, ask which way the digits will slide and how far before each button. When changing units, ask first whether the new number should be bigger or smaller. That one question settles most of this chapter.
In word problems, look for two units in the same question, such as kilograms and grams. Ask your child to write one conversion line before any adding or subtracting, and to check the unit the answer line asks for. A quick size check helps too: what is left must be less than what there was.
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