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### 2003-H: Scientific Notation 4: Metric to Scientific Notation

• Topic Cluster: Pure Mathematics
• Topic: Scientific Notation and Orders of Magnitude
• Objective: Given a metric unit, convert it to an SI unit in scientific notation
• Content:
• Level: 3

#### BACK to Ladder Scientific Notation and Orders of Magnitude

In previous pods, we learned the prefixes of the metric system and converted between standard and scientific notation. In this pod, we will convert from any metric unit to scientific notation in base units. In many reference sources and physics textbooks, information is given in non-base metric units, often because it is far more elegant to do so than to give information in non-metric units. Before completing any mathematical problem, you must convert into proper metric unit.

##### Converting from Metric to Standard Notation
1. Replace the metric prefix with an appropriate multiplier, which is always 10 to some exponent.
2. If the number returned is not in proper scientific notation, convert it to proper scientific notation using the method described in a previous pod.

### Questions

Convert each value given to its base unit in proper scientific notation.

1. I ran 12 kilometers.
2. A human hair has a width of 17 $$\mu$$meters.
3. A large city uses 12 terawatts of power.
4. The protest Eugiena gracilis has a length of 50 $$\mu$$m.
5. The color green has a frequency of 600 terahertz.
6. The color green has a wavelength of 550 nanometers.
7. The color red has a frequency of 480 terahertz.
8. The color red has a wavelength of 750 nanometers.
9. The highest sound heard by a cat has a frequency of 64 kilohertz.
10. There are 4811 kilometers on the drive from Boston to Los Angeles.

### Converting Values less than 1

1. Convert 0.55 nanometers to meters.
2. Convert 0.654 gigameters to meters
3. Convert 0.0832 milligrams to grams