GCSE Maths Practice: standard-form

Question 6 of 10

A new stadium was built at a cost of 8.9 × 10⁷ pounds. Write the cost as an ordinary number.

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\( \begin{array}{l}\text{A stadium cost }8.9 \times 10^7\text{ pounds.}\\ \text{Write this as an ordinary number.}\end{array} \)

Choose one option:

For large numbers, move the decimal right the same number of places as the exponent. Fill gaps with zeros as needed.

Converting from Standard Form to Ordinary Numbers

In GCSE Maths, standard form is used to make large and small numbers easier to work with. When a number has a positive exponent, it represents a large quantity. To convert from standard form to an ordinary number, multiply the first number (called the coefficient) by ten raised to the power shown. Each power of ten shifts the decimal point one place to the right.

Real-World Example

A new city stadium was built at a cost of 8.9 × 10⁷ pounds. In ordinary number form, that equals £89,000,000. Writing it in standard form makes it cleaner and easier to compare with other projects, such as one that costs 1.2 × 10⁸ (£120,000,000). This method avoids writing long strings of zeros and reduces the chance of misreading figures in scientific or financial data.

Step-by-Step Method

  1. Look at the exponent (the power of 10). Here it is 7.
  2. Because it’s positive, move the decimal point seven places to the right.
  3. Add zeros if there are not enough digits after the decimal.
  4. Check your final number by multiplying back to confirm.

Worked Example 1

Convert 3.2 × 10⁶.

  • Move decimal six places right → 3,200,000.
  • Result: 3,200,000.

Worked Example 2

Convert 6.45 × 10⁵.

  • Move decimal five places right → 645,000.
  • Answer: 645,000.

Worked Example 3

Convert 2.5 × 10⁴.

  • Move decimal four places right → 25,000.
  • Result: 25,000.

Common Mistakes

  • Moving the decimal the wrong way. For positive powers, always move right.
  • Counting the wrong number of places for the exponent.
  • Omitting zeros when the decimal runs out of digits.
  • Writing the coefficient incorrectly—remember it must be between 1 and 10 in standard form.

Real Applications

Large numbers like this appear in population data, finance, astronomy, and computing. For example, the UK population is around 6.8 × 10⁷, and the number of bits in 11 megabytes of data is roughly 8.8 × 10⁷. Writing such values in standard form makes calculations faster and clearer.

FAQs

  • Why is the exponent positive? Because the number is greater than one, and each power of ten increases its size.
  • Can I drop the zero after 8.9? Yes, 8.9 × 10⁷ and 8.90 × 10⁷ represent the same value, though the second shows more significant figures.
  • How can I check my result? Multiply 8.9 by 10⁷ on a calculator—if it shows 89,000,000, your answer is correct.

Study Tip

When converting, remember: a positive exponent means a big number, so move the decimal right. A negative exponent means a small number, so move it left. Memorising this pattern prevents confusion and helps you answer exam questions confidently and quickly.