# Powers of Ten Worksheets

Our entire decimal numbering system is based on the concept that each decimal place to the left is ten times greater and every place value to the right is ten times smaller than the previous spot. When we want to express values that are really small or very large, we use a similar concept. We use the concept of Power of Ten to express these types of values. A power of ten is written in the form 10^{x} where is the power (positive or negative). Writing in this format actually makes the math much more workable. You will find that this concept is the foundation of scientific notation. 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.

### Aligned Standard: Grade 8 Expressions and Equations - 8.EE.A.3

- 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?

- Answer Keys - These are for all the unlocked materials above.

### 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.

- Quiz 1 - Which is the larger value?
- Quiz 2 - Lots of different work for you.
- Quiz 3 - The end puts it all together for you.

### 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. This 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. In this case the number 10 is the focus of the powers of ten. These exponents can be negative, as well as positive.

When we are working with really small values like things found on a microscope or, better yet, an electron microscope we would use measures in negative powers of ten to quantify those values. If we were exploring the universe and describing the location of things in space, we would be working with very large values that could be explained in positive powers of ten.

Examples of non-negative and negative powers of ten are:

10 to the power zero = 10^{0} = 1

10 to the power -1 = 10^{-1} = 0.1

10 to the power 1 = 10^{1} = 10

10 to the power -2 = 10^{-2} = 0.01

10 to the power 2 = 10^{2} = 100

10 to the power -3 = 10^{-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.