Scientific Notation Mini-Lesson

Scientific Notation Mini-Lesson

How to convert between scientific notation and standard form.

Scientific Notation Definition

• A way to express numbers that are either too large or too small to be conveniently written in decimal form.

• Example:  38,000,000,000 → 3.8×10¹⁰

  
  

    

Small vs. Big #'s

• Smaller numbers have negative exponents

• Bigger numbers have positive exponents

How do we write it?

• The first number is a number greater than or equal to 1 and less than 10

• It is multiplied by a second number

• The second number is always a base of 10 with an integer exponent

Multiple Choice

Scientific notation is used to represent...

• Only Really Big Numbers

• Only Really Small Numbers

• Both Really Big and Small Numbers

• Distance

Multiple Choice

Which of the following is correct scientific notation?

• 20.35 x 10⁴

• 2035 ⁴

• .2035 x 10⁴

• 2.035 x10⁴

Multiple Choice

If the exponent is a negative number...

• You will get a large number

• You will get a small number

Multiple Choice

If the exponent is a positive number...

• You will get a large number

• You will get a small number

Multiple Choice

Convert to scientific notation:

520,000,000

• 52 x 10⁷

• 5.2 x 10⁸

• 5.2 x 10⁷

• 0.52 x 10⁹

Multiple Choice

Convert to scientific notation:

0.0005

• 50 x 10^-5

• 5 x 10³

• 5 x 10^-4

• .5 x 10³

Multiple Choice

Convert to scientific notation:

0.00071363

• 7.1363 x 10^-3

• 7.1363 x 10^-4

• 7.1363 x 10⁴

• 7.1363 x 10³

Back to Standard Form?

• Look at the exponent

• Think about if it will be a big or small number

• Move the appropriate amount of decimal places to the left or right

Multiple Choice

How would you write 5.6 x 10^-3 in standard form?

• 0.0056

• 0.00056

• 5,600

• -0.0056

Multiple Choice

How would you write 4.3756 x 10⁴ in standard form?

• 437,560,000

• 43,756

• 0.00043756

• 4,375.6

Now lets see what we've learned!

Multiple Choice

Write 0.000972 in scientific notation.

• 9.72 x 10^-4
• 9.72 x 10^-3
• 972 x 10^-4
• 9.72 x 10⁴

Multiple Choice

Write 9.8 x 10^-5 in standard form

• 0.00098
• 0.000098
• .098
• 98,000

Multiple Choice

Convert to scientific notation:
520,000,000  

• 52 x 10⁷
• 5.2 x 10⁷
• 5.2 x 10⁸
• 0.52 x 10⁹

Multiple Choice

How would you write -5.6 x 10^-3 in standard form?

• 0.0056
• -5,600
• 0.00056
• -0.0056

Multiple Choice

Express the following in scientific notation:
0.0000002203

• .02203 x 10⁷
• 22.03 x 10^-6
• 2.203 x 10^-7
• 22.03 x 106

Multiple Choice

Convert to standard notation:
3.05 x 10⁵ 

• 305,000
• 305
• 3,050,000
• 30,500

Multiple Choice

Express the following in scientific notation:

.000457

• 457 x 10⁶

• 457 x 10^-6

• 4.57 x10⁴

• 4.57 x 10^-4

Multiple Choice

Convert to standard notation:
2.4 x 10^-3 

• 2400
• 0.24
• 0.024
• 0.0024

Multiple Choice

Express the following in scientific notation:

.000457

• 457 x 10⁶

• 457 x 10^-6

• 4.57 x10⁴

• 4.57 x 10^-4

Multiple Choice

Which of the following in the LARGEST number?

• 9 x 10⁶

• 8 x 10¹⁰

• 1.3 x 10¹²

• 5.3 x 10³

Multiple Choice

Which of the following numbers is the SMALLEST?

• 8.7 x 10³
• 3 x 10⁴
• 1.3 x 10⁸
• 9 x 10²