1. Find `(2*10^5) * (13*10^-3)`
Solution:
| `(2*10^5) xx (13*10^-3)` | |
| `=(2xx13) xx (10^5xx10^-3)` | (Group the numbers) |
| `=26 xx (10^(5 + -3))` | `("law of indices " a^m xx a^n=a^(m+n))` |
| `=26xx10^2` | |
| `=(2.6xx10^1)xx10^2` | (Write 26 in scientific notation) |
| `=2.6xx10^3` | |
2. Find `(8*10^5) * (9*10^-3)`
Solution:
| `(8*10^5) xx (9*10^-3)` | |
| `=(8xx9) xx (10^5xx10^-3)` | (Group the numbers) |
| `=72 xx (10^(5 + -3))` | `("law of indices " a^m xx a^n=a^(m+n))` |
| `=72xx10^2` | |
| `=(7.2xx10^1)xx10^2` | (Write 72 in scientific notation) |
| `=7.2xx10^3` | |
3. Find `(5*10^-4) * (6*10^-3)`
Solution:
| `(5*10^-4) xx (6*10^-3)` | |
| `=(5xx6) xx (10^-4xx10^-3)` | (Group the numbers) |
| `=30 xx (10^(-4 + -3))` | `("law of indices " a^m xx a^n=a^(m+n))` |
| `=30xx10^-7` | |
| `=(3xx10^1)xx10^-7` | (Write 30 in scientific notation) |
| `=3xx10^-6` | |
This material is intended as a summary. Use your textbook for detail explanation.
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