Standard form 2 (Edexcel GCSE Maths): Revision Notes

Step-by-Step Process for Multiplication

Step 1: Rearrange so powers of 10 are together

• Group the number parts together and the power parts together
• Example: $(3 \times 10^3) \times (5 \times 10^6)$ becomes $(3 \times 5) \times (10^3 \times 10^6)$

Step 2: Multiply the number parts

• Simply multiply the decimal numbers together
• $3 \times 5 = 15$

Step 3: Add the powers

• Use the rule: $a^m \times a^n = a^{m+n}$
• $10^3 \times 10^6 = 10^{3+6} = 10^9$

Step 4: Rewrite in standard form if necessary

• $15 \times 10^9 = 1.5 \times 10^1 \times 10^9 = 1.5 \times 10^{10}$

Step-by-Step Process for Division

Step 1: Rearrange so powers of 10 are together

• Separate the number parts from the power parts
• Example: $(1.2 \times 10^6) \div (2 \times 10^4)$ becomes $(1.2 \div 2) \times (10^6 \div 10^4)$

Step 2: Divide the number parts

• Perform the division of decimal numbers
• $1.2 \div 2 = 0.6$

Step 3: Subtract the powers

• Use the rule: $a^m \div a^n = a^{m-n}$
• $10^6 \div 10^4 = 10^{6-4} = 10^2$

Step 4: Rewrite in standard form if necessary

• $0.6 \times 10^2 = 6 \times 10^{-1} \times 10^2 = 6 \times 10^1$

Step-by-Step Process for Addition/Subtraction

Step 1: Write both numbers as ordinary numbers

• Convert each standard form number to its full decimal form
• Example: $3.9 \times 10^5 = 390,000$ and $2.5 \times 10^4 = 25,000$

Step 2: Add or subtract normally

• Perform the arithmetic operation on the ordinary numbers
• $390,000 + 25,000 = 415,000$

Step 3: Convert the answer back into standard form

• Write the result in proper standard form notation
• $415,000 = 4.15 \times 10^5$

Essential Exam Strategies

• When unsure about which operation to use, try the calculation with simpler numbers first
• Always check if your final answer needs converting to proper standard form
• For real-world problems, pay attention to units and convert as necessary
• Show all steps clearly in exam answers for maximum marks