# Multiplying by Powers of 10 Worksheets

This is one of those topics that is super easy, if you understand the core concept fully. It is also super confusing if you are even slightly off center with the topic. This particular topic focuses on multiplying by various powers of ten. This means that we are greatly amplifying the values and the decimal point is moving to the right for each power we are multiplying by. If it is two powers of ten, it is two movements to the right. I would also encourage teachers to review the concept of exponents and know values of values raised to the exponent of zero and one. This will make everything fall in line well for students. This assembly of lessons and worksheets will help students strive to understand and use the concept of powers of ten.

### Aligned Standard: Grade 5 Base Ten - 5.NBT.2

- Exponents in Action Step-by-step Lesson- Let's explain exponents to kids now. While we're at it, make it a multiplication problem. Who makes up this curriculum?
- Guided Lesson - A series of nice repetition exercises, I find that working with these types of activities really helps it sink in.
- Guided Lesson Explanation - I might have spaced this one out too much. Sorry about that.
- Practice Worksheet - A monster collection of problems. Take it slow.
- Matching Worksheet - We run right off of the lesson version for this one.

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

### Homework Sheets

Remember to count the exponents as extra zeroes. That should make it a quicker task for you.

- Homework 1 - How do you write 2.3 x 10
^{2}in standard form? - Homework 2 - Multiply 10 x 0.6. Remember that when it comes to working with powers of ten, it is all about adjusting the decimal point.
- Homework 3 - Find the missing numbers across a series like this: ______ x 3 = 6, _____ x 3 =60, _____ x 3 = 600

### Practice Worksheets

We delve a bit into expanded form and products here to add a bit more difficulty.

- Practice 1 - Complete all the problems. They will come at you from many different directions.
- Practice 2 - A real mix of questions for you. Determine what is being asked to you from all the different layers.
- Practice 3 - The fill ins are the hardest to work with.

### Math Skill Quizzes

I constantly see these skills as main stays of the fifth grade curriculum, an important skill to master.

- Quiz 1 - Carry out all the product operations that you come across here.
- Quiz 2 - It is all about where those decimals end up going.
- Quiz 3 - Focus on lining everything up first here and then move on to working things up to the next level.

### What is Meant by Powers of Ten?

Ever imagined how billions and trillions would have looked if they were written out? Imagine having to work with complex and complicatedly large values, such as these, and writing them down over and over. The thought alone is tiring, isn't it? Also, writing down all those zeros is a bit intimidating. However, the introduction of the power system has made it easy to deal with big numbers. Our number system is called the base ten system which defines the values of every integer in a number. Starting from the right, each integer is ten times greater as we move to the left.

Using powers as abbreviations of such large numbers is the best way to solve even the most difficult of problems. In mathematics, the concept of power is a positive integer that represents the number of times the number has been multiplied by itself. Here it is important to keep in mind that these power integers can be negative as well as positive. The powers of then is a helpful method that we can use to write out very large or small values. You will find these used on the small side for measurements in most since labs. You we find hugely magnified in the realm of environment science that attempts to quantify very large values.

According to the definition, number one represents the zeroth power of ten. First few results of non-negative powers of ten are:

10 to the power zero = 1, 10 to the power 1 = 10, 10 to the power 2 = 100, 10 to the power 3 = 1,000, 10 to the power 4 = 10,000, 10 to the power 5 = 100,000. It can also go in the opposite direction when it comes to smaller value such as: 10^{-2} = 0.01, 10^{-3} = 0.001

The easiest way to convert these abbreviated numbers is to move the decimal to the right side, which is always before the number if not placed anywhere else. In case of negative power integers, move the decimal to the left to get the answer.