Standard Form

Standard Form with Operations

Lesson Objectives

Define standard form and understand its usefulness.
Convert ordinary numbers to and from standard form.
Add, subtract, multiply, and divide numbers expressed in standard form.
Apply these skills to practical examples.

Introduction

Standard form uses powers of 10 to express very large or small numbers succinctly: $A \times 10^b$ , with $1 \le A < 10$ and $b$ an integer.

Core Lesson Content

1. Converting to and from Standard Form

Example 1: 2345 → $2.345 \times 10^3$

Example 2: 0.00005 → $5 \times 10^{-5}$

Example 3: $3.45 \times 10^{-2} = 0.0345$

Example 4: $8.91 \times 10^6 = 8,910,000$

2. Adding & Subtracting in Standard Form

Example 5:
$(3.45 × 10^{-4}) + (2.55 × 10^{-3})$
Align exponents: $2.55 × 10^{-3} = 25.5 × 10^{-4}$
Sum: $(3.45 + 25.5) × 10^{-4} = 28.95 × 10^{-4} = 2.895 × 10^{-3}$

Example 6:
$(7.2 \times 10^5) - (1.8 \times 10^4)$
Convert: $1.8 \times 10^4 = 0.18 \times 10^5$
Difference: $(7.2 - 0.18) \times 10^5 = 7.02 \times 10^5$

3. Multiplication in Standard Form

Example 7:
$(4.5 \times 10^3) \times (2 \times 10^4)$
Multiply A's: 4.5 × 2 = 9.0. Add exponents: 3 + 4 = 7.
Result: $9.0 \times 10^7$

Example 8:
$(6 × 10^{-2}) × (5 × 10^{-3})$
6×5=30; exponent: -2+(-3)=-5 → $30 × 10^{-5} = 3.0 × 10^{-4}$

4. Division in Standard Form

Example 9:
$(9 \times 10^8) \div (3 \times 10^2)$
Divide A's:9÷3=3. Subtract exponents:8–2=6 → $3 \times 10^6$

Example 10:
$(4.2 × 10^{-5}) ÷ (2 × 10^{-8})$
4.2÷2=2.1; exponent: –5 – (–8) = +3 → $2.1 \times 10^3$

Exercises

Convert 234,000 to standard form.
Convert 0.00000789 to standard form.
[WAEC] Add $(3.45 × 10^{-4}) + (2.15 × 10^{-5})$ . (Past Question)
[NECO] Subtract $(7.2 \times 10^5) - (1.2 \times 10^4)$ . (Past Question)
Multiply $(4.5 \times 10^3) \times (3 \times 10^2)$
Divide $(9 \times 10^7) \div (3 \times 10^4)$
[JAMB] Add $(1.2 × 10^{-3}) + (3.8 × 10^{-4})$ . (Past Question)
Multiply $(6 × 10^{-2}) × (5 × 10^{-3})$
Divide $(4.2 × 10^{-5}) ÷ (2 × 10^{-8})$
[WAEC] Convert 0.000345 to standard form. (Past Question)

Conclusion

You’ve learned to convert numbers to/from standard form and perform addition, subtraction, multiplication, and division—all useful skills for scientific notation and real-world applications involving large or tiny values.