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PSLE Mathematics · Primary 5 and 6

Decimals

Decimals are another way of writing fractions with denominators of 10, 100 and 1000. In upper primary you round decimals, multiply and divide them by whole numbers and by 10, 100, 1000 and their multiples, and convert between units such as kilograms and grams. Money, length, mass and volume questions all depend on decimals, so careful place value work protects marks across the whole PSLE paper. This guide covers each skill with short examples, a worked problem and practice questions.

What the syllabus expects

  • Read place values up to 3 decimal places, and compare and order decimals
  • Round decimals to the nearest whole number, 1 decimal place or 2 decimal places
  • Multiply and divide decimals by 10, 100, 1000 and their multiples without a calculator
  • Multiply and divide decimals by whole numbers
  • Convert between fractions and decimals
  • Convert measurements such as kilometres and metres, kilograms and grams, and litres and millilitres using decimals
  • Solve word problems involving money and measures in decimal form

Place value, comparing and rounding

In 3.465, the 4 stands for 4 tenths (0.4), the 6 for 6 hundredths (0.06) and the 5 for 5 thousandths (0.005). To compare decimals, line up the decimal points and compare digit by digit from the left. So 0.8 is greater than 0.75, because 8 tenths is more than 7 tenths, even though 0.75 has more digits. To round, look at the digit just after the place you are rounding to. If it is 5 or more, round up, otherwise leave the digit as it is. So 3.465 is 3.5 to 1 decimal place, 3.47 to 2 decimal places and 3 to the nearest whole number. Rounding money to 2 decimal places gives the answer to the nearest cent. Keep any zero that rounding produces at the end, as in 4.0 to 1 decimal place, because it shows the accuracy that was asked for.

Multiplying and dividing by 10, 100 and 1000

Multiplying by 10, 100 or 1000 moves every digit 1, 2 or 3 places to the left, which looks like the decimal point moving to the right: 0.374 × 100 = 37.4. Dividing moves the digits to the right: 52.6 ÷ 1000 = 0.0526. For multiples such as 300 or 40, split the number into two easier steps. For example, 2.15 × 300 = 2.15 × 3 × 100 = 6.45 × 100 = 645, and 8.4 ÷ 40 = 8.4 ÷ 4 ÷ 10 = 2.1 ÷ 10 = 0.21. Estimating first catches errors in counting places. 2.15 × 300 is about 2 × 300 = 600, so 645 is sensible, while 64.5 or 6450 cannot be right.

Multiplying and dividing by whole numbers, and converting fractions

To multiply a decimal by a whole number, multiply as if there were no decimal point, then place the point so the answer has the same number of decimal places as the decimal you started with. For 4.36 × 7, work out 436 × 7 = 3052, then place the point to give 30.52. For division, keep the decimal point in line in long division and add zeros when you need more digits: 9.3 ÷ 6 = 1.55, and you can check that 6 × 1.55 = 9.3. A fraction becomes a decimal by division, so 3/8 = 3 ÷ 8 = 0.375. Fractions whose denominators divide into 100 can be renamed quickly: 7/20 = 35/100 = 0.35 and 3/25 = 12/100 = 0.12. Going the other way, 0.45 = 45/100 = 9/20.

Converting units of measurement

Learn these: 1 km = 1000 m, 1 m = 100 cm, 1 kg = 1000 g and 1 ℓ = 1000 ml. Changing a bigger unit into a smaller unit means multiplying, because you need more of the small units: 2.35 kg = 2.35 × 1000 g = 2350 g. Changing a smaller unit into a bigger unit means dividing: 750 ml = 750 ÷ 1000 ℓ = 0.75 ℓ. Mixed measures follow the same rule. 3 km 40 m is 3.04 km, not 3.4 km, because 40 m is 40 thousandths of a kilometre. Similarly, 5 m 8 cm is 5.08 m. Before you add, subtract or compare quantities, change them into the same unit, and state the unit the question wants in your final answer.

Worked example

A bottle holds 1.25 ℓ of juice and costs $3.85. Mrs Lim buys 6 bottles and pays with a $50 note. She pours all the juice equally into 30 cups. (a) How much change does she receive? (b) How many millilitres of juice are in each cup?

  1. Cost of 6 bottles = 6 × $3.85. Work out 385 × 6 = 2310, then place the point to give $23.10.
  2. Change = $50 − $23.10 = $26.90.
  3. Total juice = 6 × 1.25 ℓ = 7.5 ℓ (125 × 6 = 750, with 2 decimal places gives 7.50).
  4. Convert to millilitres by multiplying by 1000, because litres are the bigger unit: 7.5 × 1000 = 7500 ml.
  5. Juice in each cup = 7500 ÷ 30 = 250 ml.
  6. Check: 250 × 30 = 7500 ml = 7.5 ℓ, and $23.10 + $26.90 = $50.

Answer: (a) $26.90 (b) 250 ml in each cup.

Common mistakes

  • Moving the decimal point the wrong number of places. 0.07 × 1000 = 70, not 7 or 700. Count one place for each zero in 10, 100 or 1000, and estimate to check.
  • Writing 3 km 40 m as 3.4 km. 40 m is 40/1000 km = 0.040 km, so the answer is 3.04 km.
  • Dividing when you should multiply in a conversion. Bigger unit to smaller unit means multiply (1.2 kg = 1200 g), smaller unit to bigger unit means divide (1200 g = 1.2 kg).
  • Thinking a decimal with more digits is larger. 0.125 is smaller than 0.2 because 1 tenth is less than 2 tenths.
  • Rounding in the middle of the working. Keep the full value until the last step, then round once to the accuracy asked for.
  • Writing money as $4.5 instead of $4.50. Money answers in dollars and cents always have 2 decimal places.

Exam tips

  • Estimate every decimal calculation with rounded numbers first, then compare your exact answer with the estimate to catch a misplaced decimal point.
  • Convert all measures into one unit at the start of a problem, and write the unit beside every line of working.
  • When a question mixes money and measures, answer each part with its own unit, such as $26.90 and 250 ml, and give money to 2 decimal places.

Practice questions

1. Easy: Round 16.958 to (a) 2 decimal places (b) 1 decimal place.

Show answer

(a) 16.96 (b) 17.0. Working: for 2 decimal places, the thousandths digit is 8, so round the 5 hundredths up to 6. For 1 decimal place, the hundredths digit is 5, so round 9 tenths up, which carries into the ones and gives 17.0.

2. Medium: 2.4 kg of sugar is packed equally into 8 bags. What is the mass of sugar in each bag in grams?

Show answer

300 g. Working: 2.4 ÷ 8 = 0.3 kg, and 0.3 × 1000 = 300 g.

3. Harder: A carpenter has a plank 3.6 m long. He cuts off 5 pieces, each 0.48 m long. He then cuts the rest of the plank into pieces, each 15 cm long. How many 15 cm pieces does he get?

Show answer

8 pieces. Working: 5 × 0.48 m = 2.4 m. The rest is 3.6 − 2.4 = 1.2 m = 120 cm. Then 120 ÷ 15 = 8.

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