Exponents and scientific notation study guide answer key

File Type

PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
1.98 MB   |   5 pages

PRODUCT DESCRIPTION

Test Prep Study Guide for 8.EE.A.1 through 8.EE.A.4.

• Two Pages that Copy Perfectly Front to Back
• Answer Key Included
• Fill in the Blank Style Study Guide with Corresponding Practice Problems
• Study Guide Sections Include:
  • Vocabulary
  • Exponent Rules
  • Square and Cube Roots
  • Writing in Scientific Notation
  • Operations in Scientific Notation

*****************************************************************************

Interested in More Test Prep for 8th Grade Math? Check these out in my store now:

Countdown to Test Prep Practice/Bellwork

8th Grade Math Test Prep Bundle

*****************************************************************************

Customer Tips:

How to get TPT credit to use on future purchases:

• Please go to your My Purchases page (you may need to login). Beside each purchase you'll see a Provide Feedback button. Simply click it and you will be taken to a page where you can give a quick rating and leave a short comment for the product. Each time you give feedback, TPT gives you feedback credits that you use to lower the cost of your future purchases. I value your feedback greatly as it helps me determine which products are most valuable for your classroom so I can create more for you. ☺

Be the first to know about my new discounts, freebies and product launches:

• Look for the green star next to my store logo and click it to become a follower. Voila! You will now receive email updates about this store. ☺

*****************************************************************************

1. Write 0.000078 in scientific notation.

A. 7.8 x 10-5
B. 7.8 x 10-4
C. 7.8 x 10-3
D. 7.8 x 104
E. 7.8 x 105

2. Multiply. Write the answer in exponential form.

46 . 43

A. 42
B. 48
C. 49
D. 412
E. 418

3. Simplify the expression.

4. Simplify the expression.

5. Write 8,000,000 in scientific notation.

A. 8 x 104
B. 8 x 105
C. 8 x 106
D. 80 x 104
E. 80 x 105

6. Divide.

A. 2y2
B. 2y9
C. 8y2
D.8y9
E. 8y18

7. Write in standard notation.

2.84 x 104

A. 0.000284
B. 0.00284
C. 2.840000
D. 2,840
E. 28,400

8. Simplify the expression.

A. a-12
B. a-7
C. a
D. a7
E. a12

9. Simplify the expression.

A. 3x7
B. 3x12
C. 9x7
D. 9x12
E. 27x12

10. Divide.

12a8 / 3a2

A. 3a4
B. 3a6
C. 4a4
D. 4a6
E. 9a4

Answer Key

1. A. Scientific notation is a way of conveniently writing numbers that are either very large or very small. A number written in scientific notation has two parts as shown below: a number a that is between 1 and 10 (excluding 10) and a power of ten.

a x 10b

Examine the given number. For a, use the first digits that are not zero and place the decimal after the first digit. The value of a is 7.8.

Next find the exponent. Since 0.000078 is a very small number, the exponent will be negative. Count the number of places you need to move the decimal point from its original place until it is between the 7 and the 8. Since you move the decimal point five places, the exponent will be -5. Therefore, the correct answer is 7.8 x 10-5.

2. C. To multiply the exponential terms, use the product rule, xa . xb = xa+b . Since the bases of the factors are the same, multiply them by adding the exponents.

3. E. This expression can be simplified by using exponent rules. First distribute the exponent (the 3 outside the parentheses) over the numerator and denominator in the fraction.

Next, there are two exponent rules that you can use to simplify the expression further: (1) you can distribute the exponents over each factor in the numerator and the denominator, and (2) you can use the power rule, (xa)b = xa.b. Keep in mind that the a in the numerator is equivalent to a1 because anything to the first power is itself.

4. D. To divide the exponential terms, use the quotient rule,

5. C. Scientific notation is a way of conveniently writing numbers that are either very large or very small. A number written in scientific notation has two parts as shown below: a number a that is between 1 and 10 (excluding 10) and a power of ten.

a x 10b

Examine the given number. For a, use the first digits that are not zero and place the decimal after the first digit. The value of a is 8.0, or simply 8.

Next find the exponent. Since 8,000,000 is a very large number, the exponent will be positive. Count the number of places the decimal point must move from its original place until it is between the 8 and the first 0. Since the decimal point moves six places, the exponent becomes 6. Therefore, the correct answer is 8 x 106.

6. D. To divide by a fraction, invert the fraction by switching the numerator and denominator.

Now multiply normally. Multiply the coefficients and variables separately. To multiply the variables, use the power rule, (xa)b = xa.b.

7. E. Standard notation is the normal way of writing numbers in decimal form. The given number is written in scientific notation. It has two parts: a decimal number and an exponential term. To convert it to standard notation, move the decimal. Since the exponent is positive 4, move the decimal four places to the right. Add zeros to the end as needed.

8. E. This expression can be simplified by using two exponent rules. First apply the power rule, (xa)b = xa.b .

By definition,

9. E. There are two exponent rules that you can use to simplify the expression further. First distribute the exponents over each factor in the parentheses

Next simplify each factor. Calculate the value of 33 and use the power rule, (xa)b = xa.b, to simplify the variable factor.

10. D. Start by rewriting the problem as a fraction.

Next, simplify the fraction. Divide the coefficients and the exponential terms separately. To divide the exponential terms, use the quotient rule,

How do you do exponents in scientific notation?

What is the correct scientific notation for 10000 quizlet?

How to scientific notation?

What is 0.000345 expressed in scientific notation?