GCSE Maths Practice: standard-form

Question 8 of 10

The speed of sound is approximately 9.5 × 10² metres per second. Express this as an ordinary number.

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\( \begin{array}{l}\text{The speed of sound is }9.5 \times 10^2\text{ m/s.}\\ \text{Write this as an ordinary number.}\end{array} \)

Choose one option:

For positive powers of ten, move the decimal to the right. Each power represents one zero added to the number.

Converting Standard Form into Ordinary Numbers

Standard form allows us to express both very large and very small numbers in a compact and manageable way. When a number has a positive power of ten, it represents a value greater than one. Converting back to an ordinary number is simple—you multiply the first part (called the coefficient) by ten for each step of the exponent.

Real-World Example

The speed of sound in air is approximately 9.5 × 10² metres per second. This means the sound wave travels around 950 m/s through the air. Expressing it in standard form is convenient for comparing with other speeds, such as light (3.0 × 10⁸ m/s) or water waves (1.5 × 10¹ m/s). Converting to ordinary form lets us see the actual scale more clearly.

How to Convert Step by Step

  1. Look at the exponent of ten—in this case, 2.
  2. Because it is positive, move the decimal point to the right twice.
  3. Fill any empty spaces with zeros if necessary.
  4. The new value is the ordinary number: 950.

Worked Example 1

Convert 4.8 × 10³.

  • Move decimal three places right → 4800.
  • Answer: 4800.

Worked Example 2

Convert 2.3 × 10⁴.

  • Move decimal four places right → 23000.
  • Result: 23,000.

Worked Example 3

Convert 7.06 × 10².

  • Move decimal two places right → 706.
  • Answer: 706.

Common Mistakes

  • Moving the decimal the wrong way (left instead of right for positive powers).
  • Writing 95 or 9500 by miscounting the decimal shifts.
  • Forgetting zeros when there are not enough digits to move through.
  • Mixing up positive and negative exponents—positive exponents increase the number.

Applications in Science

Standard form is vital in scientific measurement. Physicists express distances, masses, and speeds this way to compare very different scales easily. For example, the diameter of Earth (1.27 × 10⁷ m) and a paper’s thickness (1 × 10⁻⁴ m) can both be handled in the same consistent format. Converting between standard and ordinary numbers strengthens your understanding of place value and scale.

FAQs

  • Why move the decimal right? Because multiplying by powers of ten increases the number’s value.
  • Can I write 9.50 × 10² instead? Yes—it shows the same number with an extra significant figure.
  • How do I check? Multiply the coefficient (9.5) by 10² on a calculator to confirm 950.

Study Tip

Remember: a positive exponent means the number grows larger. Count carefully—each power adds one zero if no digits remain. Practising both directions (standard to ordinary and ordinary to standard) will make conversions automatic during your GCSE Maths exam.