Standard form 1 (Edexcel GCSE Maths): Revision Notes
Standard form 1
What is standard form?
Standard form is a way of writing very large or very small numbers in a more convenient format. It's particularly useful in science and mathematics when dealing with extreme values.
Numbers written in standard form follow this structure:
Where:
- a is a number that must be greater than or equal to 1 and less than 10
- represents a power of 10, where n can be positive or negative
Standard form is also known as scientific notation in some regions. This notation allows scientists and mathematicians to work with extremely large numbers (like distances in space) or extremely small numbers (like atomic measurements) in a manageable way.
When to use positive and negative powers
Understanding when to use positive or negative powers is crucial for correctly converting numbers:
Critical Rule for Powers:
-
Large numbers (greater than 10): Use a positive power of 10
- Example: 920,000 becomes
-
Small numbers (less than 1): Use a negative power of 10
- Example: 0.00703 becomes
Converting to standard form using decimal places
The counting decimal places method helps you convert between ordinary numbers and standard form:
For large numbers:
- Count how many places the decimal point needs to move to create a number between 1 and 10
- This gives you the positive power of 10
- Example: 7900 → move 3 places →
For small numbers:
- Count how many places the decimal point needs to move to create a number between 1 and 10
- This gives you the negative power of 10
- Example: 0.00035 → move 4 places →
Important tip: Don't just count zeros - count the actual decimal places moved! This is a common mistake that can lead to incorrect powers.
Using calculators with standard form
Most scientific calculators have a special key for entering standard form:
Calculator Steps:
- Look for the ×10^x or EXP key
- To enter , press: 3 7 ×10^x ( - ) 6
- Some calculators may display the answer as a regular number, so you might need to convert it back to standard form
Calculator tip: If working with standard form numbers, consider putting brackets around each number to avoid errors.
Converting from standard form to ordinary numbers
To convert from standard form back to an ordinary number, follow this directional rule:
- If the power is positive: Move the decimal point right
- If the power is negative: Move the decimal point left
- Move the decimal point the exact number of places shown in the power
Worked Example: Converting
Step 1: Identify the power: (negative) Step 2: Move decimal point 3 places to the left Step 3:
Worked examples
Worked Example: Converting to Standard Form
Large number: 1,630,000
- Count decimal places: 6 places to the left
- Result:
Small number: 0.00028
- Count decimal places: 4 places to the right
- Result:
Worked Example: Converting to Ordinary Numbers
From :
- Power is negative, so move decimal 3 places left
- Result: 0.0042
From :
- Power is positive, so move decimal 5 places right
- Result: 391,000
Calculations with standard form:
When adding or multiplying numbers in standard form, you can:
- Use a calculator (remember to convert final answers back to standard form if needed)
- Apply normal arithmetic rules while keeping track of powers of 10
Key Points to Remember:
- Standard form structure: Always where
- Big numbers (>10) use positive powers of 10
- Small numbers (<1) use negative powers of 10
- Count decimal places to find the correct power
- Calculator tip: Use brackets around standard form numbers in calculations
- Always check your final answer makes sense compared to the original number