Standard Form Calculations
Year 9 🔢 Number Add, subtract, multiply and divide numbers in standard form.
🔢 Standard Form Recap
Standard form (scientific notation) writes numbers as $a \times 10^n$ where $1 \leq a < 10$ and $n$ is an integer.
Large number: $3{,}700{,}000 = 3.7 \times 10^6$
Small number: $0.00042 = 4.2 \times 10^{-4}$
➕ Multiplying and Dividing in Standard Form
Multiply or divide the $a$ values, then add or subtract the powers of 10.
Multiply: $(3 \times 10^4) \times (2 \times 10^3) = 6 \times 10^7$
Divide: $\frac{8 \times 10^5}{2 \times 10^3} = 4 \times 10^2$
After multiplying, check that the result is still in standard form. If the $a$ value is 10 or more, adjust: $12 \times 10^4 = 1.2 \times 10^5$.
➕ Adding and Subtracting in Standard Form
Convert to the same power of 10 first, then add or subtract the $a$ values.
Example: $3 \times 10^5 + 4 \times 10^4 = 3 \times 10^5 + 0.4 \times 10^5 = 3.4 \times 10^5$
⚡ Real-World Scale
| Quantity | Standard Form |
|---|---|
| Distance to the Sun | $1.5 \times 10^{11}$ m |
| Mass of an electron | $9.1 \times 10^{-31}$ kg |
| Speed of light | $3 \times 10^{8}$ m/s |
Ready to test yourself? Click the Quiz tab above to answer questions on this topic!
Interactive Demonstration — Standard Form Calculations
🎬
Interactive demonstration available in the Calculator tab!
🔢 Standard Form Calculator
Perform arithmetic on numbers in standard form.