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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

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Lesson Transcript

Instructor:
*Jennifer Beddoe*

Most numbers can be written in different ways, either as a fraction, decimal or exponent. This lesson will teach you how to write fractions and decimals using exponents and how to convert between the two.

When you look back at pictures of yourself, do you ever stop and notice just how much you've changed? You might be skinnier, taller, have longer hair or even different color hair, but no matter how your appearance changes, you are still the same person. You are always you.

An **exponent** is a superscript number whose purpose is to indicate how many times the main number (or base) should be multiplied to itself.

In this example, the superscript '2' tells us to multiply the base '5' to itself two times, or 5 * 5, which is equal to 25.

Exponents can also be written with a carat, like this: 5^2.

**Negative exponents** are a bit different. They still indicate how many times to multiply a number to itself, but it also means that the base is on the wrong side of the fraction line, which means that if the negative exponent is in the **numerator** (top of a fraction), to make it positive, it needs to be switched to the **denominator** (bottom of a fraction).

3^-2 = 1 / 3^2

The reverse is also true. If the negative exponent is in the denominator, to make it positive, just move it to the numerator.

1 / 2^-5 = 2^5

Just like you are still the same person whether you have long hair or short hair, are fat or thin, the mathematical expression is the same regardless of whether it's written as a fraction, decimal or with a negative exponent.

So, 3^-3 can also be written as 1 / 3^3 or 1/27. It can also be written as a decimal. To write a fraction as a decimal, you just need to divide - in this case, divide 1 by 27 to get 0.037.

Let's try another one.

Write 4^-2 as a fraction and as a decimal.

First, to write it as a fraction, we know that the negative exponent will become positive when placed in the denominator of a fraction. So, we know that:

4^-2 = 1 / 4^2 = 1/16

Then, to write 1/16 as a decimal, simply divide.

1/16 = 0.0625

It even works with variables.

*b*^-5 = 1 / *b*^5

1 / *y*^-8 = *y*^8

Let's do one last example.

Write this term using only positive exponents. Simplify where possible.

(*x*^-8 * 3^3) / (4^-2 * *y*^2)

The first thing we can do is switch every term with a negative exponent to the opposite side of the fraction. *x*^-8 will move to the denominator, and 4^-2 will move to the numerator.

Then our term looks like this:

(4^2 * 3^3) / (*x*^8 * *y*^2)

To simplify, we can multiply out the numbers with exponents. 4^2 becomes 16, and 3^3 is 27. Finally, we can multiply 27 and 16 to get:

432 / (*x*^8 * *y*^2)

Just as the essence of you doesn't change just because your appearance does, so numbers, even though they are written in a different form, don't change what they are. A number can be written as a fraction, decimal and in some cases with exponents. To convert a number with a negative exponent to one with a positive exponent, simply place it on the other side of a fraction line. So, *x*^-7 becomes 1 / *x*^7.

After you've completed this lesson, you should be able to:

- Describe how to write a number in fraction and in decimal form and explain why this does not change what the number is
- Explain how to convert a number with a negative exponent to one with a positive exponent

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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

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