Standard Form

Summary and Exam Tips for Standard Form

Standard Form is a subtopic of Number, which falls under the subject Mathematics in the Edexcel Lower Secondary curriculum. It is a concise method to represent very large or very small numbers. In standard form, a number is expressed as $A \times 10^n$, where $A$ is a number between 1 and 10, and $n$ is a whole number indicating how many places the decimal point moves. For example, $3.2 \times 10^6$ is in standard form.

To convert from standard form to ordinary numbers, such as $4.2 \times 10^5$, move the decimal point 5 places to the right, resulting in 420,000. Conversely, for a negative exponent like $2.8 \times 10^{-4}$, move the decimal point 4 places to the left to get 0.00028.

When converting ordinary numbers to standard form, like 56,700,000, shift the decimal point left until the number is between 1 and 10, resulting in $5.67 \times 10^7$. For small numbers like 0.0000099, move the decimal right to get $9.9 \times 10^{-6}$.

Exam Tips

• Understand the Structure: Remember that in standard form, $A$ must be between 1 and 10, and $n$ is the number of decimal places moved.
• Practice Conversions: Regularly practice converting between standard form and ordinary numbers to build confidence.
• Watch the Signs: Pay attention to the direction of the decimal movement; left for positive $n$ and right for negative $n$.
• Use Examples: Familiarize yourself with examples to quickly identify patterns and apply them in exams.
• Check Your Work: Always double-check your calculations, especially the placement of the decimal point and the power of 10.