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### 2003-I: Scientific Notation 5: Scientific Notation to Metric

• Topic Cluster: Pure Mathematics
• Topic: Scientific Notation and Orders of Magnitude
• Objective: Convert from numbers written in scientific notation with SI units to more elegant metric units
• Content:
• Level: 3

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

In the previous pod, we learned how to convert from a metric system unit to a correct unit. In this pod, we will do the reverse, convert from a scientific notation value into other metric unit.

#### Part 1: The order of magnitude is already a multiple of 3.

Replace the exponent part of each problem with the necessary metric prefix.

1. $$3.69 \times 10^{12} \text{ meters}$$
2. $$8.12 \times 10^6 \text{ meters}$$
3. $$1.47 \times 10^{15} \text{ Hertz}$$
4. $$3.14 \times 10^{-6} \text{ meters}$$
5. $$5.67 \times 10^{-15} \text{ Watts}$$
6. $$3.87 \times 10^{-12} \text{ meters}$$

#### Steps

1. Move the decimal point to right RIGHT and DECREASE* the exponent until the exponent is a multiple of 3.
2. Replace the exponent with the necessary metric prefix.

Make sure that in the end, your significant figures are not less than one.

1. $$4.56 \times 10^{11} \text{ Watts}$$
2. $$3.87 \times 10^7 \text{ Joules}$$
3. $$8.15 \times 10^{10} \text{ Hertz}$$
4. $$3.59 \times 10^{-5} \text{ meters}$$
5. $$6.45 \times 10^{-10} \text{ meters}$$
6. $$3.38 \times 10^{-7} \text{ meters}$$

#### Part 3: Smaller orders of magnitude

In all honesty, none of the metric prefixes for powers smaller than +3 or -3 are used frequently, with the exception of centimeters. These prefixes are deca, hecto, deci, and centi. However, they do sometimes appear, and you are certianly free to use them yourself!

The method of converting these is similar to the methods in the very fast conversions.

Convert each of the following to a metric unit.

1. Convert 0.68 meters to centimeters.
2. Convert 12 meters to hectometers.
3. Convert 0.145 grams to centigrams.
4. Convert 88.3 Newtons to decanewtons.
5. Convert 0.891 metets to decimeters.
6. Convert 888 Watts to hectowatts.

### Answers:

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

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