GCSE Maths Practice: standard-form

Question 7 of 10

The distance from the Earth to the Moon is about 1,230,000,000 metres. Express this in standard form.

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\( \begin{array}{l}\text{The distance from Earth to the Moon is }1\,230\,000\,000\text{ m. Write this in standard form.}\end{array} \)

Choose one option:

For large numbers, move the decimal to the left until the first number is between 1 and 10. Use a positive exponent for the number of moves.

Representing Large Numbers in Standard Form

Standard form makes it easier to handle extremely large values that would otherwise require many zeros. In GCSE Maths, this skill is particularly useful in scientific topics such as astronomy, population studies, and data measurement. When a number is greater than ten, we move the decimal point to the left until the first part of the number lies between 1 and 10. The number of moves becomes the positive power of ten.

Real-World Example

The average distance from the Earth to the Moon is approximately 1,230,000,000 metres. Writing this in standard form gives 1.23 × 10⁹ m. Using powers of ten allows scientists to record and compare such distances efficiently without writing all the zeros. The same principle applies to astronomical distances, for example, 1.5 × 10¹¹ m from the Earth to the Sun.

Step-by-Step Method

  1. Write the number in full (e.g., 1,230,000,000).
  2. Move the decimal point left until the first digit is between 1 and 10.
  3. Count the number of moves (here, nine).
  4. Write this as 1.23 × 10⁹.

Worked Example 1

Convert 67000000 to standard form.

  • Move decimal seven places left → 6.7.
  • Exponent = 7.
  • Result: 6.7 × 10⁷.

Worked Example 2

Convert 4900000000 to standard form.

  • Move decimal nine places left → 4.9.
  • Exponent = 9.
  • Answer: 4.9 × 10⁹.

Worked Example 3

Convert 820000 into standard form.

  • Move decimal five places left → 8.2.
  • Exponent = 5.
  • Result: 8.2 × 10⁵.

Common Mistakes

  • Forgetting that the first number must be between 1 and 10.
  • Using a negative exponent for large numbers (it should be positive).
  • Miscounting decimal places when moving left.

Where Standard Form is Used

Scientists, engineers, and geographers use standard form constantly. Astronomers express planetary distances; biologists describe large populations or bacteria counts; computer engineers use it when discussing memory in gigabytes or terabytes. It provides clarity and prevents confusion across different disciplines and measurement systems.

FAQs

  • Why is the exponent positive? Because the number is larger than one and the decimal moved left.
  • Can I write 12.3 × 10⁸ instead? No — the number before the × must be between 1 and 10. The correct version is 1.23 × 10⁹.
  • How can I check my answer? Multiply 1.23 × 10⁹ to get 1,230,000,000.

Study Tip

When dealing with large values, count the zeros in groups of three to make moving the decimal easier. For example, one billion (1,000,000,000) has nine zeros, so its exponent is 9. Practise writing common large numbers like one million (10⁶) and one billion (10⁹) until you remember them instantly.