Standard form 1 (AQA GCSE Maths): Revision Notes
Standard form 1
What is standard form?
Standard form is a way of writing very large or very small numbers more simply. It's also called scientific notation.
Numbers in standard form are written as the product of two parts:
Where:
- a is a number greater than or equal to 1 and less than 10
- n is an integer (whole number) power of 10
For example:
You can use standard form to write very large or very small numbers more easily. This is particularly useful in scientific calculations where you might encounter extremely large numbers (like distances in space) or extremely small numbers (like atomic measurements).
Converting to standard form
Large numbers (bigger than 10)
When converting large numbers to standard form, the power of 10 is positive.
For any number greater than 10, you'll move the decimal point to the left, which gives you a positive exponent.
Converting Large Numbers to Standard Form
Convert 920000 to standard form:
- Start with: 920000
- Move decimal point to get a number between 1 and 10: 9.2
- Count decimal places moved: 5 places left
- Result:
Small numbers (smaller than 1)
When converting small numbers to standard form, the power of 10 is negative.
For any number less than 1, you'll move the decimal point to the right, which gives you a negative exponent.
Converting Small Numbers to Standard Form
Convert 0.00703 to standard form:
- Start with: 0.00703
- Move decimal point to get a number between 1 and 10: 7.03
- Count decimal places moved: 3 places right
- Result:
Counting decimal places method
The decimal places method is a reliable way to convert between numbers in standard form and ordinary numbers. This method focuses on counting the actual movement of the decimal point rather than just counting zeros.
Converting from ordinary to standard form:
Large numbers: Count how many places the decimal point moves left
- (3 jumps left, so power is positive 3)
Small numbers: Count how many places the decimal point moves right
- (4 jumps right, so power is negative 4)
Be careful! Don't just count zeros to work out the power. Count the actual decimal place movements. This is a common mistake that can lead to incorrect answers.
Using a calculator
Most scientific calculators have a special key for entering numbers in standard form.
You can enter numbers in standard form using the ×10^n key (sometimes labelled EXP or EE).
Calculator Input Method
To enter , press: 3 → . → 7 → ×10^n → - → 6
Top tip: If you're using a calculator with numbers in standard form, put brackets around each number to avoid mistakes with order of operations.
Your calculator might give the answer as a normal number. You need to convert it into standard form if the question requires it.
Worked examples
Worked Example: Converting to Standard Form
Question: Write 1630000 in standard form.
Solution: Step 1: Count the decimal places you need to move to get a number between 1 and 10. Step 2: 1630000 is bigger than 10, so the power will be positive. Step 3: Move decimal point 6 places left:
Answer:
Worked Example: Converting from Standard Form
Question: Write as an ordinary number.
Solution: Step 1: The negative power means the number is small (less than 1). Step 2: Move the decimal point 3 places to the left. Step 3:
Answer: 0.0042
Worked Example: Calculations with Standard Form
Addition/Subtraction: Convert to ordinary numbers first, then calculate
Multiplication/Division: You can work directly with the standard form
Exam tips
Exam Success Tips
- Always check whether your answer should be in standard form or as an ordinary number
- Count decimal places carefully - don't just count zeros
- Use brackets when entering standard form numbers into your calculator
- Remember: big numbers have positive powers, small numbers have negative powers
- Double-check your working by converting your answer back to ordinary form
Summary
Key Points to Remember:
- Standard form is written as where and is an integer
- Large numbers (greater than 10) have positive powers of 10
- Small numbers (less than 1) have negative powers of 10
- Count decimal places to find the power - don't just count zeros
- Use brackets when entering standard form into calculators to avoid errors