Edexcel Mathematics (4XMAH) -Unit 2 - 1.9 Standard Form- Study Notes- New Syllabus
Edexcel Mathematics (4XMAH) -Unit 2 – 1.9 Standard Form- Study Notes- New syllabus
Edexcel Mathematics (4XMAH) -Unit 2 – 1.9 Standard Form- Study Notes -Edexcel iGCSE Mathematics – per latest Syllabus.
Key Concepts:
A solve problems involving standard form
Edexcel iGCSE Mathematics -Concise Summary Notes- All Topics
Standard Form
Standard form is used to write very large or very small numbers in a compact way.
\( a\times10^n \)
where:
- \( 1\le a<10 \)
- \( n \) is an integer
Examples
\( 4500000=4.5\times10^6 \)
\( 0.00032=3.2\times10^{-4} \)
Multiplying in Standard Form
Multiply the numbers and add the powers:
\( (a\times10^m)(b\times10^n)=ab\times10^{m+n} \)
Dividing in Standard Form
Divide the numbers and subtract the powers:
\( \dfrac{a\times10^m}{b\times10^n}=\dfrac{a}{b}\times10^{m-n} \)
Addition and Subtraction
First write both numbers with the same power of 10, then add or subtract.
Example 1:
\( (3\times10^5)(4\times10^3) \)
▶️ Answer/Explanation
\( 3\times4=12 \)
\( 10^{5+3}=10^8 \)
\( 12\times10^8=1.2\times10^9 \)
Conclusion: \( 1.2\times10^9 \).
Example 2:
\( \dfrac{6\times10^7}{3\times10^2} \)
▶️ Answer/Explanation
\( 6\div3=2 \)
\( 10^{7-2}=10^5 \)
\( 2\times10^5 \)
Conclusion: \( 2\times10^5 \).
Example 3:
\( 2.4\times10^6 + 5\times10^5 \)
▶️ Answer/Explanation
Make powers equal:
\( 5\times10^5=0.5\times10^6 \)
\( 2.4\times10^6+0.5\times10^6=2.9\times10^6 \)
Conclusion: \( 2.9\times10^6 \).