## Patterns in Products with Many Zeros

#### Aligned To Common Core Standard:

**Grade 5 Base Ten** - 5.NBT.2

**What is Meant by Powers of Ten?**
Ever imagined how billions and trillions would have looked if written? Imagine having to work with complex and complicatedly large 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.
Using powers as abbreviations of such large numbers is the best way to solve even the most difficult of problems. In mathematics, the 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.
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 zeroth = 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
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.

### Printable Worksheets And Lessons

- 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.

#### 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
- Homework 2 - Multiply 10 x .6
- Homework 3 - Find the missing numbers. ______ 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.
- Practice 2 - A real mix of questions for you.
- Practice 3 - The fill ins are the hardest.