Choose exam board for KS4 Computer Science (GCSE)
Choose exam board for KS4 English
Choose exam board for KS4 French
Choose exam board for KS4 Geography
Choose exam board for KS4 German
Choose exam board for KS4 History
Choose tier for KS4 Maths
Choose exam board for KS4 Music
Choose exam board for KS4 Physical education (GCSE)
Choose exam board for KS4 Religious education (GCSE)
Choose exam board for KS4 Spanish

      Accuracy of final answers

      Lesson details

      Learning outcome

      I can appreciate the accuracy in leaving an answer without carrying out the final operation.

      Key learning points

      1. There is always a choice regarding how you represent a value.
      2. You need to consider the most suitable way for the situation.
      3. Rounding reduces accuracy so a rounded answer is not always useful.
      4. There are agreed forms: one operation remaining and the result of the operation would produce a non-terminating decimal.
      5. Surd form is one such acceptable way.

      Keywords

      • Recurring decimal - A recurring decimal is one that has a digit or sequence of digits that repeat endlessly.

      • Terminating decimal - A terminating decimal is one that has a finite number of digits after the decimal point.

      • Rational number - A rational number is one that can be written in the form a/b where a and b are integers and b is not equal to 0.

      • Irrational number - An irrational number is one that cannot be written in the form a/b where a and b are integers and b is not equal to 0.

      • Surd - A surd is an irrational number expressed as the root of a rational number.

      Common misconception

      Surds are any number with a root symbol.

      √4 is not a surd as it is equivalent to 2.

      Teacher tip

      Pupils may struggle with 0 not being a natural number. Natural numbers are positive whole numbers. 0 is neither positive nor negative and therefore cannot be a natural number.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

      Loading...

      Prior knowledge starter quiz

      6 Questions

      Q1.
      Which of these numbers is not a whole number?

      12
      16
      7
      Correct answer: 2.3

      Q2.
      Press the $$\pi$$ button on your calculator. What is the sixth digit?

      Correct answer: 9
      6
      5
      2

      Q3.
      Enter $$\sqrt{5}$$ on your calculator. What is the second digit?

      Correct Answer: 2, two

      Q4.
      A circle has a diameter of 3 cm. What is the circumference of the circle to 1 decimal place?

      Correct Answer: 9.4, 9.4 cm

      Q5.
      Enter $$\sqrt[3]{64}$$ on your calculator. What is the answer?

      Correct Answer: 4, four

      Q6.
      Which of these is an example of a recurring decimal?

      1.2
      1.252525253
      Correct answer: $$1.\dot{6}$$
      2.222

      6 Questions

      Q1.
      True or false? The group of integers includes negative numbers.

      Correct answer: True
      False

      Q2.
      A number is one that can be written in the form $$a \over b$$ where $$a$$ and $$b$$ are both integers and $$b \ne 0$$.

      Correct Answer: rational

      Q3.
      Identify the rational number.

      $$\pi$$
      Correct answer: 0.263
      $$\sqrt 3$$
      $$\sqrt 2$$

      Q4.
      Which of these is a surd?

      Correct answer: $$\sqrt {21}$$
      $$\sqrt {25}$$
      $$\sqrt {36}$$
      $$\sqrt {49}$$

      Q5.
      Which of these is a surd?

      $$\sqrt[3] {64}$$
      $$\sqrt[3] {27}$$
      Correct answer: $$\sqrt[3] {16}$$
      $$\sqrt[3] 8$$

      Q6.
      Which of these is a surd?

      $$\sqrt {1 \over 25}$$
      $$\sqrt {0.25}$$
      Correct answer: $$\sqrt {1 \over 6}$$
      $$\sqrt {1 \over 49}$$

      To help you plan your 10 maths lesson on: Accuracy of final answers, download all teaching resources for free and adapt to suit your pupils' needs...