Lesson 1: Introduction to Scientific Notation
What is Scientific Notation?
Sometimes numbers are very, very big, like the distance from the Earth to the Sun. Other times, numbers are very, very small, like the size of a tiny germ. Writing all the zeros can be confusing and hard to read. Scientific notation is a way to write very large or very small numbers more simply using powers of 10.
A power of 10 is a number like 10, 100, 1,000, or 0.1, 0.01, 0.001, coming from multiplying or dividing by 10 many times.
For example:
- 1,000,000 = 10 × 10 × 10 × 10 × 10 × 10 = 10⁶
- 0.001 = 1 ÷ 10 ÷ 10 ÷ 10 = 10⁻³
So instead of writing 1,000,000, we can write 1 × 10⁶. This is easier to read and compare.
Recap
Scientific notation helps us write very big and very small numbers more simply.
We always use a number between 1 and 10 multiplied by a power of 10.
- Large numbers → positive exponents (10², 10³, 10⁶…).
- Small numbers → negative exponents (10⁻¹, 10⁻², 10⁻⁵…).
Examples
1. Write 5 million in standard form.
1 million = 1,000,000. So, 5 million = 5,000,000.
2. Write 10 million in standard form.
10 million = 10,000,000.
3. Write 13 million in standard form.
13 million = 13,000,000.
4. Write 6.8 million in standard form.
Move the decimal 6 places → 6.8 → 6,800,000.
5. Write 1.4 hundred million in standard form.
100,000,000 × 1.4 = 140,000,000.
6. Write 1.21 hundred million in standard form.
100,000,000 × 1.21 = 121,000,000.
7. Write 5.11 ten million in standard form.
10,000,000 × 5.11 = 51,100,000.
8. Write 49.5 million in standard form.
Move the decimal 6 places → 49.5 → 49,500,000.
Table Example
| Planet | Approximate Diameter (m) | Standard Form |
|---|---|---|
| Mercury | 5 million | 5,000,000 |
| Venus | 10 million | 10,000,000 |
| Earth | 13 million | 13,000,000 |
| Mars | 6.8 million | 6,800,000 |
| Jupiter | 1.4 hundred million | 140,000,000 |
| Saturn | 1.21 hundred million | 121,000,000 |
| Uranus | 5.11 ten million | 51,100,000 |
| Neptune | 49.5 million | 49,500,000 |
9. Write 300 in scientific notation.
300 = 3 × 10².
10. Write 9,000 in scientific notation.
9,000 = 9 × 10³.
11. Write 10,000,000 in scientific notation.
10,000,000 = 1 × 10⁷.
12. Write 0.03 in scientific notation.
0.03 = 3 × 10⁻².
13. Write 0.006 in scientific notation.
0.006 = 6 × 10⁻³.
14. Write 0.00008 in scientific notation.
0.00008 = 8 × 10⁻⁵.
15. Round 77,249 to the nearest ten thousand.
Thousands digit = 7 → round up → 80,000.
16. Write 80,000 in scientific notation.
80,000 = 8 × 10⁴.
17. Round 0.0710 to the nearest hundredth.
Hundredths digit = 7. Thousandths digit = 1 (<5). Answer = 0.07.
18. Write 0.07 in scientific notation.
0.07 = 7 × 10⁻².
19. Round 1,253,679 to the nearest million.
Hundred thousands digit = 2 (<5). Answer = 1,000,000.
20. Write 1,000,000 in scientific notation.
1,000,000 = 1 × 10⁶.
21. Round 0.00000000028 to the nearest ten billionth.
Ten billionth digit = 2. Next digit = 8 (≥5) → round up → 0.0000000003.
22. Write 0.0000000003 in scientific notation.
0.0000000003 = 3 × 10⁻¹⁰.
23. Match the multiplication with the exponent.
10 × 10 = 10²
10 × 10 × 10 = 10³
10 × 10 × 10 × 10 = 10⁴