GCSE Maths Practice: standard-form

Question 4 of 10

Practise converting small decimal numbers into standard form without revealing the specific answer.

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\( \begin{array}{l}\text{Convert } 0.0049 \text{ to standard form.}\end{array} \)

Choose one option:

Count how many decimal places you move and apply a negative power of ten if the number is less than one.

Understanding Standard Form

Standard form, or scientific notation, is a common way of writing very small or very large numbers in a shorter and clearer form. Instead of writing out many zeros, you express the number as a value between 1 and 10 multiplied by a power of ten. This approach is widely used in GCSE Maths, as well as in science and engineering, where extremely large or small values often appear.

Why We Use Standard Form

Numbers like 0.000034 or 67000000 are difficult to read and easy to misinterpret. Standard form eliminates this issue. For example, scientists might write the distance between atoms or the mass of planets using powers of ten. It improves accuracy and helps when comparing quantities across different scales.

How to Convert to Standard Form

  1. Find the position of the decimal point in the number.
  2. Move the decimal so that the number becomes between 1 and 10.
  3. Count how many places you moved the decimal point.
  4. If the number was smaller than 1, use a negative power. If it was larger than 1, use a positive power.

Worked Example 1

Convert 0.0081 to standard form.

  • Move the decimal three places right → 8.1
  • The power of ten is −3
  • Result: 8.1 × 10⁻³

Worked Example 2

Convert 3400 to standard form.

  • Move the decimal three places left → 3.4
  • The power of ten is +3
  • Answer: 3.4 × 10³

Worked Example 3

Convert 0.00062 to standard form.

  • Move the decimal four places right → 6.2
  • Power of ten is −4
  • Final: 6.2 × 10⁻⁴

Common Errors to Avoid

  • Forgetting to make the first number between 1 and 10.
  • Getting the sign of the exponent wrong (negative for numbers smaller than one).
  • Counting decimal movements incorrectly.
  • Writing zeros unnecessarily in the coefficient (the first part before the × sign).

Real-World Applications

Standard form appears in every scientific and technological field. Astronomers use it to describe distances between stars, such as 4.2 × 10¹⁶ metres. Biologists describe bacteria sizes as around 2 × 10⁻⁶ metres. Financial analysts use it to represent exchange rates and market values. Even computers rely on similar principles when handling floating-point numbers in programming languages like Python or JavaScript.

FAQs

  • Can standard form be used with negative numbers? Yes, the coefficient can be negative, for example −3.5 × 10².
  • Is there a difference between scientific notation and standard form? They mean the same thing, though the UK uses the term ‘standard form’ more commonly in GCSE Maths.
  • Do I always need to round? Usually yes — exam questions often ask for a specific number of significant figures.

Study Tip

When practising conversions, focus on estimating whether the final number should be bigger or smaller than one. This helps you choose the correct sign for the power. To build confidence, try converting both extremely large and extremely small numbers every day. Understanding the pattern of decimal movement will make any standard form question feel natural in your GCSE Maths exam.