E2.1 Represent very large (mega, giga, tera) and very small (micro, nano, pico) metric units using models, base ten relationships, and exponential notation.
Activity 1: Representing Very Large and Very Small Units (Base Ten Relations and Exponential Notation)
Complete the table below on the order of magnitude of very large and very small numbers. Refer to a metric units table to help you. What do you notice? The first row is filled in for you as an example.
|
Number |
Basic Unit |
How Many Times Is the Number Larger or Smaller than the Base Unit? |
Express the Number Using Exponential Notation |
|
7 kilograms |
gram |
The kilogram is 1000 times larger than the gram. |
7 × 103 grams |
|
3 picolitres |
|||
|
5 megawatts |
|||
|
4 nanometers |
|||
|
6 terabits |
I notice that:
Source: translated from En avant, les maths!, 8e année, ML, Sens de l’espace, p. 4.
Activity 2: Comparison of Very Large and Very Small Metric Units
- The distance between two atoms is 300 pm and the distance between the Earth and the Sun is 150 Gm. How many times greater is the latter than the former? Express your answer in exponential notation.
- It is said that ants can lift up to 1000 times their weight. If an ant weighs 10 mg, and a bumblebee weighs 0.4 g, can the ant lift the bumblebee? Show your calculations.
- Light travels about one metre in 3 ns. How many metres can it travel in one year (one light-year)?