GCSE Maths Practice: standard-form

Question 3 of 10

Learn how to convert small decimals into standard form for GCSE Maths without revealing the final value.

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\( \begin{array}{l}\text{Convert } 0.00045 \text{ to standard form.}\end{array} \)

Choose one option:

Shift the decimal to make a number between 1 and 10, then count the moves to find the correct power of ten.

Understanding Standard Form

In GCSE Maths, standard form (or scientific notation) is a clear way to represent very large or very small numbers. It writes numbers as a value between 1 and 10 multiplied by a power of 10. This notation makes comparisons, calculations, and data presentation much simpler. For instance, scientists prefer standard form because it avoids long strings of zeros, making results easier to read and less prone to errors.

When to Use Standard Form

Whenever a number is extremely large (like 300,000,000) or very small (like 0.0000003), standard form gives a shorter, more convenient version. In exams, it helps display answers neatly and ensures the correct number of significant figures is shown.

How to Convert to Standard Form

  1. Find where the decimal point needs to move so that the first part of the number is between 1 and 10.
  2. Count the number of places moved — this number becomes the power of 10.
  3. If the original number was smaller than 1, use a negative power. If it was larger than 1, use a positive power.

Worked Example 1

Convert 0.0063 into standard form.

  • Move the decimal three places right → 6.3
  • Power of ten is −3
  • Result: 6.3 × 10⁻³

Worked Example 2

Convert 52,000 into standard form.

  • Move decimal four places left → 5.2
  • Power of ten is +4
  • Result: 5.2 × 10⁴

Worked Example 3

Convert 0.000072 into standard form.

  • Move decimal five places right → 7.2
  • Power of ten is −5
  • Answer: 7.2 × 10⁻⁵

Common Mistakes

  • Writing the first number outside the 1–10 range (e.g., 12 × 10³).
  • Confusing positive and negative powers. Remember: negative exponents mean smaller than one.
  • Miscounting decimal movements. Always double-check with a calculator or by expanding back.

Real-Life Applications

Standard form is used across science and finance. Chemists write molecular sizes in 10⁻⁹ m, astronomers express distances in 10¹¹ m, and engineers describe microvolt or megawatt ranges the same way. It’s also used in computer storage units, population studies, and physics equations such as E = mc².

FAQs

  • Why do we use powers of ten? Because our number system is base-10, each movement of the decimal corresponds to multiplying or dividing by 10.
  • Can a number in standard form start with zero? No. The first digit must be 1–9 to stay within the 1–10 range.
  • What’s the difference between 10⁻³ and 10³? The first makes a number smaller (÷1000), the second makes it larger (×1000).

Study Tip

Always estimate whether the answer should be larger or smaller than one before deciding the sign of the power. Practising with both small and large numbers builds intuition and prevents sign errors during your GCSE Maths exam.