Practical Application for Scientific Measurement & Dimensional Analysis

Instructor: Julie Zundel

Julie has taught high school Zoology, Biology, Physical Science and Chem Tech. She has a Bachelor of Science in Biology and a Master of Education.

While math can look scary, this lesson will provide you with step-by-step instructions on significant figures, scientific notation, and unit conversion. Plus, you'll see why math is so important in science.

Numbers in Science

Science and numbers go together like peanut butter and jelly. Yep, math and science are the BFFs of the academic world. We will explore some of the math utilized in science, along with some practice problems, so you can see how the two are intertwined.

Significant Figures

Let's start our exploration with significant figures, which is how scientists show the accuracy of an answer. For example, an answer of 12 vs. 12.00 shows a difference in measuring tools.

For all of our practice problems, we will need to write our answers using the correct number of significant figures, so go over the rules before we move on:

  • All non-zero numbers are significant. For example, 154 has three significant figures.
  • Zeros between non-zero numbers are significant. For example, 103 has three significant figures.
  • A zero to the left of a non-zero significant figure is NOT significant. For example, 0.004 has one significant figure.
  • If a zero is at the end of a number to the right of a decimal, it is significant. For example, 12.0 has three significant figures.

Now that we know the rules of significant figures, let's dive right in.

Scientific Notation

In science, numbers can be really big and really small. For example, did you know that Pluto is 3,670,050,000 miles from the sun, or that some viruses are only 0.0000002 centimeters in diameter?

Writing all of those digits takes time and can lead to errors (did I add enough zeros?), so scientists use scientific notation, which is a way to write large and small numbers in a more convenient form, or N x 10a.

Some rules regarding scientific notation:

  • N is a number between 1 and 10 (but not 10)
  • The exponent, a, is the number of places the decimal was moved.
  • If a is negative, the decimal was moved to the right.
  • If a is positive, the decimal was moved to the left.

Now that you know the rules, let's get started.

Problem #1: Scientific Notation

Write 140,000,000,000 in scientific notation.

  • Step 1:

Before we start, we should note how many significant figures we are dealing with because this will impact our answer. The number 140,000,000,000 has two significant figures. As a result, we will make sure N has two significant figures.

  • Step 2:

Now let's solve. Move the decimal so N is between 1 and 10 with two significant figures. In this case that would be 1.4. Note: if no decimal is present, you can assume it's after the last number or 140,000,000,000.

Count up how many times you move the decimal and the direction. You can see we moved it 11 times to the left.

Moving the decimal 11 spots to the left to make 1.4
Scientific Notation

  • Step 3:

Since you moved it to the left 11 spaces, a will be a positive 11, so the answer is 1.4 x 1011.

Metric System Conversion

The scientific world utilizes the metric system or a measurement system that uses multiples of 10 as ways to convert between units. This is a good thing, since it's relatively easy to convert between units. There are different basic units, depending upon what you are measuring. Some of the base units are as follows:

  • Length: meter
  • Volume: liter
  • Mass: gram

There are prefixes that show how much of a basic unit you have. For example, the prefix milli means 0.001 of a base unit. In other words, if we are dealing with volume, a milliliter is 0.001 of a liter. We will utilize this table that shows the prefixes and what they represent.

Kilo 1,000 Hecto 100 Deka 10 Basic Unit Deci 0.1 Centi 0.01 Milli 0.001

The rules for converting between the units is fairly straightforward. If you move to the right on the table (i.e. converting between hecto and milli), you can move the decimal to the right. If you are converting from left to right (i.e. converting between a centi and a kilo), you can move the decimal to the left. Let's try this out.

Problem #2: Converting between metric units

Convert 5.99 kilometers to centimeters

  • Step 1:

Determine how many significant figures are in 5.99. Hmmmm… Looks like three.

  • Step 2:

Use your table to determine how many places you will have to move the decimal and note the direction.

  • Step 3:

Using this information, move the decimal over five spots to the right, adding zeros if no numbers are present.

Move the decimal five places to the right

  • Step 4:

Write the answer and make sure you have the right number of significant figures. The answer is 599,000 centimeters, which has three significant figures. If you look at the starting number, 5.99, it also had three, so we wrote the answer correctly.

Dimensional Analysis

Sometimes converting between units is not as easy as moving decimal points, so another option is called dimensional analysis, which is a method of converting between units that uses ratios and fractions. Before we do a practice problem, let's discuss the steps:

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