ExamSolutions Maths

Number

# Standard Form

🤓 Study

📖 Quiz

Play audio lesson

Standard Form

Understanding Standard Form

**Standard form**, also known as scientific notation or exponential notation, is a way of writing or displaying large or small numbers compactly.- It is represented as
**a × 10^n**, where 1 ≤ a <10 and 'n' is an integer. - The value 'a' is called the
**mantissa**and 'n' is called the**exponent**or power. - Positive 'n' means the decimal point moves to the right, indicating a large number.
- Negative 'n' means the decimal point moves to the left, indicating a small number.

Converting to Standard Form

- If the number is already in decimal form, place the decimal point such that the number becomes between 1 and 10. This number becomes the mantissa.
- Count the number of places you moved the decimal point. This will be your exponent.
- If you moved the decimal to the left, the exponent is positive. If to the right, the exponent is negative.

Converting from Standard Form

- Look at the exponent. If it's positive, move the decimal point in the mantissa to the right. If it's negative, move the point to the left.
- Make sure to add zeros as placeholders if needed.

Calculations in Standard Form

- When
**adding or subtracting**numbers in standard form, they should have the same exponent. If not, convert them so they do before performing the operation. - To
**multiply**or**divide**numbers in standard form, multiply or divide the mantissas and add or subtract the exponents, respectively.

Application of Standard Form

- Standard form is often used to represent very large quantities such as distances in space or very small sizes such as the size of atoms.
- It's also used to simplify calculations and make them more manageable.

Common Mistakes to Avoid

- Forgetting that the decimal point in the mantissa should be after the first digit.
- Miscounting the number of places moved when finding the exponent.
- When adding or subtracting, forgetting to make sure the exponents are the same.
- Not considering the direction of the decimal point movement when determining the sign of the exponent.