Scientific Notation Worksheet Library

Free Scientific Notation Worksheets with Answer Keys

Welcome to our Scientific Notation Worksheet Library, where you can access a free collection of practice worksheets that can be downloaded as printable PDF files.

Each free scientific notation worksheet shared in the library below includes a variety of practice problems and/or word problems related to scientific notation, and each worksheet includes a complete answer key.

You can easily preview download any scientific notation worksheet by clicking on any of the blue text links in the worksheet library below. When you click on a text link, a preview window will open where you can inspect the worksheet and answer key, as well as save the PDF file to your device or sent the file to your printer.

This page also includes a Scientific Notation Review Section, where will will recap some key concepts and vocabulary terms as well as a few step-by-step example problems that are similar to the practice problems on many of our scientific notation worksheets. If you find yourself struggling with any of the worksheets offered in our library below, we highly recommend visiting this section to sharpen your skills before moving forward.

The free worksheets in the library below are all samples from the Mashup Math Infinite Math Worksheet Libraries for Grades K-12. If you want more PDF practice worksheets for tons of math topics, visit our website to access the full library. | Guide: How to Download/Print

Scientific Notation Worksheet Library

▶️ Scientific Notation Word Problems (A)

▶️ Scientific Notation Word Problems (B)

▶️ Practice with Scientific Notation (A)

▶️ Practice with Scientific Notation (B)

▶️ Practice with Scientific Notation (C)

▶️ Extended Practice: Scientific Notation (A)

▶️ Extended Practice: Scientific Notation (B)

▶️ Extended Practice: Scientific Notation (C)

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Scientific Notation Worksheet Review

In this section, we will review everything you need to know about scientific notation in order to solve the types of problems you will find on the practice worksheets in the library above.

In math, scientific notation refers to a simple and useful way to express and work with numbers that are either extremely large or extremely small. For example, if you were expressing the distance between two planets in kilometers, you could use scientific notation instead of writing out an extremely large number. On the other hand, if you wanted to describe the diameter of a skin cell, you could use scientific notation instead of writing out an extremely small number. Whether you are dealing with large numbers, small numbers, or anything in between, scientific notation is an incredibly important and useful math tool with applications far beyond the classroom.

So, how does scientific notation work and what does it look like?

Scientific notation is a uniform way of expressing numbers, large or small, as the product of a number and a power of 10. Any number expressed in scientific notation will be of the form:

• a × 10ⁿ, where a is a positive number and n is an integer.

For example, the number 4,800 can be expressed using scientific notation as follows:

• 4,800 = 4.8 × 10³

Note that the scientific notation expression is just another way to express the number 4,800. If we actually performed the multiplication of the scientific notation form, we would see that:

• 4.8 × 10³ = 4.8 × 1,000 = 4,800

As for small numbers, consider the example 0.0079. We can express this number using scientific notation as follows:

• 0.0079 = 7.9 × 10⁻³

Notice that, in this example, our exponent is a negative number.

In the case of scientific notation and the corresponding exponent:

• Large numbers will have a positive exponent (e.g. 10⁷) and you will move the decimal point to the left.

• smaller numbers will have a negative exponent (e.g. 10⁻⁴) and you will move the decimal point to the right.

Scientific Notation Worksheet Examples

Example #1: Write the following number using Scientific Notation: 1,400,000

First, start by identifying the coefficient (the value of a) by shifting the decimal point to the left until it is directly in front of the first non-zero digit. In this case, we have:

• 1,400,000 → a = 1.4

Next, count how many place value slots that you had to move the decimal to achieve this result to find the value of n. In this case, we had to shift the decimal point 6 place value slots to the left as follows:

• 1, 4 0 0, 0 0 0 . 0 → 1.400000 → n = 6

Now we are ready to write our number in scientific notation (a × 10ⁿ form) using a=1.4 and n=6 as follows:

• 1,400,000 = 1.4 × 10⁶

We have now successfully expressed the number 1,400,000 in scientific form as 1.4 × 10⁶.

Example #2: Write the following number using Scientific Notation: 0.000000813

In this example, we are dealing with a very small number. However, the process is still the same.

Start by identifying the value of a by shifting the decimal point to the right until it is directly in front of the first non-zero digit. In this case, we have:

• 0.000000813 → a = 8.13

Next, count how places that you had to move the decimal to find the value of n. In this example, we shifted the decimal point 7 place value slots to the right as follows:

• 0 . 0 0 0 0 0 0 8 . 1 3 → 8.13 → n = 7

Finally, we can express the number in scientific notation (a × 10ⁿ form) using a=8.13 and n=7 as follows:

• 0.000000813 = 8.13 × 10⁻⁷

The entire step-by-step process for solving this second example is shown in Figure 02 below.