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Copyright © Swun MathCopyright © Swun Math (^) Grade 8 Unit 3 Lesson 2 P TE

Homework

Unit 3 · Lesson 2: Scientific Notation

Objective: I will use the scientific notation to write very large and very small numbers.

Vocabulary Steps

Scientific Notation: a method to write very large

numbers or very small numbers as the product of

a number between 1 and 10 and a power of 10

99 = 9.9 × 101

Power of Ten: ten multiplied by itself the

number of times indicated by the exponent

To figure out power of 10, think “How many places does the decimal

point move?”

If number is 10 or greater,

move to the left = positive power

If number is less than 1,

move to the right = negative power

1. Ask yourself, “Is my number big or small?”
   
   
   • Big number = positive power
   
   
   • Small number = negative power
   
   
   
   


2. Move the decimal point so that you have a
   number between 1 and 10.


3. Count how many times you moved the
   decimal to determine the power.


4. Write expression using scientific notation.

Scientific Notation to Standard Form:

1. If the exponent is positive, move to the right
   (multiplication).


2. If the exponent is negative, move to the left
   (division).


3. Make additional zeros for place value needed.

Example # 1 Example # 2

Directions: Convert number into scientific notation. Directions: Convert number into standard notation.

The news report had 40,000,000 people watching.

Solution:

• The decimal needs to be between the 4 and 0.


• This means that the decimal needs to be moved 7 places to the
  left: 4.0


• The new number is less than the original number. The
  exponent needs to be a positive.

Answer: 4 × 107

The chemist found 6.8 × 10–^8 traces of chlorine in the water.

Solution:

• Since the power of 10 is negative, divide by a base of 10. 10 −8=
  1
  108


• Divide 6.8 by 100,000,000.


• This means move the decimal to the left. Add zeros if spaces
  are needed.


• 6.8 × 10 –8 = 0.000000068

Answer: 0.000000068

Name: ___

Date: ___