Decimals

Decimals are another way of writing parts of a whole, and they are everywhere: prices at the canteen, times at the swimming carnival, distances on a road trip and readings on a rain gauge. In this topic you'll learn what each digit after the decimal point is worth, use all four operations with decimals, switch between fractions and decimals, and round answers to a sensible accuracy. You'll also use estimates to check that your answers make sense.

What you'll learn

• 5.01 Decimals and place value: tenths, hundredths and thousandths, expanded form, and comparing and ordering decimals.
• 5.02 Add and subtract decimals: lining up the decimal points, mental strategies, and estimating to check.
• 5.03 Convert between fractions and decimals: writing decimals as fractions in simplest form, and fractions as decimals (including ones that repeat forever).
• 5.04 Multiply decimals: multiplying by 10, 100 and 1000, counting decimal places, and using a known fact.
• 5.05 Divide decimals: dividing by 10, 100 and 1000, short division with decimals, and dividing by a decimal.
• 5.06 Round decimals: rounding to a whole number or a number of decimal places, choosing a sensible accuracy, and using estimates to check answers.

Which level should I pick?

Every worksheet comes in three levels. Each one covers the same skills.

• Level 1 · Warm-up: simpler decimals and more help along the way. A good place to start.
• Level 2 · Core: the main worksheet for the lesson.
• Level 3 · Challenge: more decimal places and problems with more steps, for when the Core level feels easy.

Not sure? Start with Level 2. If the first few questions feel tricky, drop to Level 1. If you finish quickly and get them right, try Level 3. Download the worksheet, print it, and write your answers in the boxes.

Practice tests

When you've finished the lessons, try the three practice tests. Each one is like the real topic test: 45 minutes, 40 marks, a section without a calculator and a section with one. Write your working under each question, then copy your final answers onto the answer sheet on the last page, just like you will in the real test.