EDEXCEL GCSE HIGHER MATHS - What is the Standard Form and Its Applications

Edexcel GCSE Higher Maths: Standard Form

What is Standard Form?

Standard form is a way of writing very large or very small numbers in a concise and convenient way. It follows this format:

• a x 10n

where:

• a is a number between 1 and 10 (but not including 10)
• n is an integer (a whole number)

How to Convert to Standard Form

1. Identify the decimal point.
2. Move the decimal point to the right or left until you have a number between 1 and 10. Count the number of places you moved the decimal.
3. Write the number as 'a x 10n'.
   • If you moved the decimal point to the right, 'n' will be negative.
   • If you moved the decimal point to the left, 'n' will be positive.

Examples:

• 5,200,000: Move the decimal point 6 places to the left. Result: 5.2 x 106
• 0.0000045: Move the decimal point 6 places to the right. Result: 4.5 x 10-6

How to Convert from Standard Form to Decimal Form

1. Look at the exponent (n).
2. Move the decimal point in 'a' the number of places indicated by 'n'.
   • If 'n' is positive, move the decimal point to the right.
   • If 'n' is negative, move the decimal point to the left.

Examples:

• 7.8 x 104: Move the decimal point 4 places to the right. Result: 78,000
• 2.3 x 10-3: Move the decimal point 3 places to the left. Result: 0.0023

Applications of Standard Form

Standard form is used in many scientific and mathematical applications, including:

• Astronomy: Describing the distances between stars and planets.
• Physics: Representing the size of atoms and other very small particles.
• Chemistry: Expressing the concentration of solutions.
• Engineering: Working with large values of force, pressure, and energy.

Calculations in Standard Form

• Multiplication: Multiply the 'a' values and add the exponents.
• Division: Divide the 'a' values and subtract the exponents.
• Addition and Subtraction: Convert the numbers to decimal form before performing the operation.

Example:

(2 x 105) x (3 x 103) = (2 x 3) x 10(5+3) = 6 x 108

Conclusion

Standard form is a powerful tool that allows us to express very large and very small numbers efficiently. By understanding the concept of standard form and its applications, you can confidently tackle a variety of problems in mathematics and science.