# Practice with the Metric System, Significant Figures & Scientific Notation

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• 0:03 What Is the Metric System?
• 1:15 Significant Figures &…
• 2:42 Examples of Conversions
• 4:59 Lesson Summary
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Lesson Transcript
Instructor: Michael Blosser

Michael has a Masters in Physics and a Masters in International Development. He has over 5 years of teaching experience, teaching Physics, Math, and English classes.

This lesson will introduce the reader to the metric system, significant figures, and scientific notation. Additionally, we will use those three components as a way to do metric system conversions.

## Metric System

The metric system is the system of measurement for length, mass or weight, volume, time, temperature, speed, and numerous other characteristics of objects in our world. The metric system of measurement is used by every country in the world except for the United States, Brunei, Burma, and Yemen. Another important aspect of the metric system is that it provides a base unit (such as grams, meters, liters, etcâ€¦) and uses prefixes to represent multiples of the base units that are based on the powers of ten. Here's a list of the most commonly used metric prefixes, their symbols, and the powers of 10 correlated to them:

For example, lets look at the metric system in terms of length. The meter is the base unit for the metric system of the measurement of length. If someone was 2 meters tall, we wouldn't need to use any of the prefixes, but lets say that the distance between two cities was 35,000 meters. We could also write that the distance between the two cities was 35 kilometers due to kilometers being meters to 3 powers of 10. We will explore more about metric conversions and how significant figures and scientific notation play an important part in these conversions.

## Significant Figures & Scientific Notation

As you saw, the metric prefixes used a type of notation that correlates to a power of 10. This notation is a key part of what we call scientific notation. Scientific notation is a way to write numbers, and it's particularly useful when the numbers are very big or very small. For example, the number 500 can be written in scientific notation as 5 x 102 or the number 0.002 can be written as 2 x 10-3. What scientific notation does is writes the significant figures, or sometimes called significant digits, of a number multiplied by a power of 10, which tells us where to put the decimal of the number.

Now a very important aspect of scientific notation is the significant figures of a number. But how do we determine the significant figures of a number? To determine the significant figures of a number, we need to follow these three rules:

1. Any nonzero figures are significant (1-9)
2. Any zeros between nonzero figures are significant.
3. Any zeros before or after non-zero figures are not significant if they are not between any nonzero figures.

The power of 10 tells us where to move the decimal when converting from regular numbers to scientific notation. If the number is less than 1, we move the decimal to the right and use a negative power of 10 and if the number is greater than 10 we move the decimal to the left and use a positive power of 10

## Examples of Conversions

Now, we can apply what we learned to do some conversions with the metric system. Let's make sure we use our metric prefixes, significant figures, and scientific notation.

### Example 1

First, let's write the numbers 5126 and 0.0000008 in scientific notation:

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