GCSE Maths Practice: standard-form

Question 1 of 10

A car travels 7000 metres during a speed test. Write this distance in standard form.

›

\( \begin{array}{l}\text{A car travels }7000\text{ metres.}\\ \text{Write this in standard form.}\end{array} \)

Choose one option:

For large numbers, move the decimal left until the first number is between 1 and 10. Count the moves to find the positive power of ten.

Expressing Large Numbers in Standard Form

Standard form allows large numbers to be written neatly without long strings of zeros. When a number is greater than one, its decimal point moves to the left until the first number is between 1 and 10. The number of moves determines the positive exponent for 10. This makes numbers easier to compare, especially in scientific or technical work.

Real-World Example

A car travels 7000 metres during a long-distance test. Instead of writing 7000, it can be expressed as 7.0 × 10³ metres. Using standard form helps engineers and scientists work with distances and measurements in a consistent, compact way. For instance, 1 kilometre equals 1.0 × 10³ metres, so both 7000 m and 1 km can be expressed using powers of ten.

How to Convert Step by Step

  1. Write the number clearly (7000).
  2. Move the decimal point left until the first part of the number is between 1 and 10 → 7.0.
  3. Count the number of moves (three).
  4. Attach the power of ten with a positive exponent: 7.0 × 10³.

Worked Example 1

Convert 48000 to standard form.

  • Move decimal four places left → 4.8.
  • Power = +4.
  • Answer: 4.8 × 10⁴.

Worked Example 2

Convert 1200000 to standard form.

  • Move decimal six places left → 1.2.
  • Power = +6.
  • Result: 1.2 × 10⁶.

Worked Example 3

Convert 95000 to standard form.

  • Move decimal five places left → 9.5.
  • Power = +4 (because 9.5 × 10⁴ = 95000).

Common Mistakes

  • Moving the decimal the wrong way — for large numbers, always move it left.
  • Using a negative exponent instead of a positive one.
  • Writing 70 × 10² or 0.7 × 10⁴, which are not in proper standard form (the first number must be between 1 and 10).

Everyday Applications

Standard form is widely used in science and technology. For example, Earth’s radius is about 6.4 × 10⁶ m, and the speed of sound is roughly 3.4 × 10³ m/s. Expressing quantities this way saves time and prevents mistakes when working with very large or very small measurements.

FAQs

  • Why is the exponent positive? Because large numbers require multiplying by powers of ten, not dividing.
  • Can I drop the zero after 7.0? Yes, it can be written as 7 × 10³, but 7.0 × 10³ shows two significant figures if precision matters.
  • How can I check my result? Multiply 7.0 by 10³ to confirm it returns to 7000.

Study Tip

Memorise the first few powers of ten to make conversions quick: 10³ = 1000, 10⁴ = 10000, and 10⁵ = 100000. This will save time during your GCSE Maths exam when converting between large and small numbers in standard form.