## Powers of Ten and Scientific Notation

#### Aligned To Common Core Standard:

**Grade 8 Number System** - 8.EE.A.3

What are the Powers of Ten? Even the thought of writing dealing with complex and large numbers is enough to scare you off. Writing them down over and over is a difficult and tiring thing. The thought alone is tiring. Placing the multiple zeros can take an entire lifetime. Thanks to the introduction of the power system, which has made it easy to deal with big numbers. Power system or commonly known as powers of ten features a positive integer that denotes the number of times a number has been multiplied by itself. These can be negative, as well as positive. Examples of non-negative and negative powers of ten are: 10 to the power zeroth = 1 10 to the power -1 = 0.1 10 to the power 1 = 10 10 to the power -2 = 0.01 10 to the power 2 = 100 10 to the power -3 = 0.001 The above few examples show that when the power of ten is positive, the zero moves to the right-hand side, and when the power is negative, the zeros jump to the left-hand side. These worksheets and lessons will help students become comfortable with the use of the powers of ten and how they are applied and used in scientific notation.

### Printable Worksheets And Lessons

- Scientific Notation
Step-by-Step Lesson- Sorry that I didn't add the commas to the
zeroes in the number that is presented. Some people complain about
that, but the testing often has no commas.

- Guided Lesson
- Jump between standard form, scientific notation, and comparing
powers of ten.

- Guided Lesson Explanation
- With any math problem, I always recommend getting the integers
to be treated the same. I'm a big advocate for "Integer Rights".

- Independent Practice
- The nuclear symbol throws off some people. But scientific notation
is most commonly known as the language of nuclear chemistry and
physics.

- Matching Worksheet
-I like this one because you can get kids in the habit of focusing
on the front part of notation easily with this.

- Scientific Notation
Five Pack - Make it a decimal.

- Converting Between Standard
Form and Scientific Notation Five Pack -Write it in scientific
form then change it back again.

- Write in Scientific Notation Five Pack - I go heavy on the zeroes here. Too much?

#### Homework Sheets

Decimals to scientific form for the first two homework sheets. The last sheet does the opposite.

- Homework 1 - Move the decimal point to the left until the number is between 1 and tenth place. Count how many places you move the decimal point.
- Homework 2 - This number is less than one. This tells us that every tens place we move will result in a negative exponent.
- Homework 3 - The positive exponent of 10 tells how many places to the right to move the decimal point.

#### Practice Worksheets

In addition to what students saw on the homework, we add the comparison of values.

- Practice 1 - Move the decimal point to the tight until you are between a ones and tenths place.
- Practice 2 - Write 0.0000916 in scientific notation.
- Practice 3 - Express scientific notation in standard form.

#### Math Skill Quizzes

Remember to get students in the habit of adding commas to any numbers over 999. It helps a lot.