Speed of Light in Scientific Notation
Convert 300,000 km/s into a compact number using powers of 10.
Equation
y = 1 * 10^x
Graph
Table
| x | y |
|---|---|
| 0 | 1 |
| 1 | 10 |
| 2 | 100 |
| 3 | 1000 |
| 4 | 10000 |
| 5 | 100000 |
| 6 | 1000000 |
What this lesson covers
What you do
You shape the function y = a * 10^x and watch the graph answer.
Challenges to clear
- Set a = 3. Scan the powers of ten: 300,000 sits at x = 5 — the speed of light is 3 × 10⁵ km/s.
- One power less is ten times smaller: x = 4 shows 30,000.
- A new measurement: 700,000. The digit part is 7 — slide a there.
- Now shift the powers so x = 3 lands on 700,000. In standard form that is 7 × 10⁵, so the shift c is 2.
Check yourself
Why is 300,000 written as 3 * 10^5 and not 30 * 10^4?
If the speed of sound is approximately 340 m/s, which of the following is the correct scientific notation?
- Because in scientific notation, the first number (coefficient) must be greater than or equal to 1 and less than 10. — correct
- Because 30 * 10^4 equals 300,000, so both are correct.
- Because 10^5 is a larger number than 10^4.
- Because we always start with the digit 3.
- 3.4 * 10^2 — correct
- 34 * 10^1
- 0.34 * 10^3
- 340 * 10^0