GCSE Maths Practice: standard-form

Question 5 of 10

The distance from the Earth to the Moon is about 9,000,000 millimetres.}\\ \text{Express this in standard form.

‹ ›

\( \begin{array}{l}\text{The distance from Earth to the Moon is }9\,000\,000\text{ mm. Write this in standard form.}\end{array} \)

Choose one option:

For large numbers, move the decimal left until the first number is between 1 and 10. The number of moves gives the positive exponent.

Writing Large Numbers in Standard Form

When a number is very large, writing all the zeros can be time-consuming and can easily lead to mistakes. Standard form (also known as scientific notation) helps express these numbers more simply. A number in standard form always has two parts: a value between 1 and 10 multiplied by a power of ten. The power of ten tells us how many times to multiply by 10 to get back to the full number.

Real-World Example

The distance from the Earth to the Moon is about 9,000,000 millimetres. Instead of writing all those zeros, it can be written as 9.0 × 10⁶ mm. Using standard form saves space, looks cleaner, and helps scientists make comparisons more easily. For example, the distance from the Earth to the Sun is about 1.5 × 10¹¹ m, which shows just how much larger that distance is compared to the Moon.

Step-by-Step Conversion

  1. Write the number clearly: 9,000,000.
  2. Move the decimal point left until the number is between 1 and 10.
  3. Count how many moves were made — in this case, six.
  4. Attach the power of ten: 9.0 × 10⁶.
  5. The positive exponent means the number is large (greater than 1).

Worked Example 1

Convert 1200000 into standard form.

  • Move the decimal six places left → 1.2.
  • Result: 1.2 × 10⁶.

Worked Example 2

Convert 45000000 into standard form.

  • Move decimal seven places left → 4.5.
  • Result: 4.5 × 10⁷.

Worked Example 3

Convert 62000 into standard form.

  • Move decimal four places left → 6.2.
  • Result: 6.2 × 10⁴.

Common Mistakes

  • Moving the decimal the wrong way—remember, large numbers require moving left.
  • Forgetting the rule that the first number must be between 1 and 10.
  • Using a negative power for a large number.
  • Writing 90 × 10⁵ or 0.9 × 10⁷, which are not valid forms.

Where It’s Used

Standard form is used widely across science, engineering, and mathematics. Astronomers use it to describe distances in space, physicists use it to express force or energy, and data scientists use it when handling billions of records or bytes. It keeps numbers easy to read and avoids counting long chains of zeros.

FAQs

  • Why is the exponent positive? Because the number is greater than one, and the decimal moves left.
  • Can I write 0.9 × 10⁷ instead? No, because the first number must be between 1 and 10. 9.0 × 10⁶ is correct.
  • How can I check my answer? Multiply 9.0 by 10⁶ on a calculator—it should return 9,000,000.

Study Tip

Remember: if the number is larger than one, move the decimal left and use a positive exponent. If it’s smaller than one, move it right and use a negative exponent. Regular practice with both types will help you handle standard form quickly and accurately in your GCSE Maths exam.