Scientific Notation Part I8th Grade MathBy Mr. Laws

Goal/Standards

•8.EE.4 – Use numbers expressed in the form of a single a single digit times in integer power of 10 to estimated very large or very small quantities, and to express how many times as much one is that the other.

Essential Question:

Using Math Principle, explain how I can use scientific notation to represent very large or very small numbers?

What is scientific notation?

Scientific notation is a method used in math or science to write out very large or very small quantities.

Scientific notation can be written in standard form, which are numbers or scientific notation form.

Power Base of 10• Scientific notation must be written based on the powers of

10.

Positive Negative

101 = 10 10-1 = 0.1

102 = 100 10-2 = 0.01

103 = 1,000 10-3 = 0.001

104 = 10,000 10 -4 = 0.0001

105 = 100,000 10-5 = 0.00001

106 = 1,000,000 10-6 = 0.000001

Etc... Etc…

Smaller Number

s

Larger Numbers

What does writing in scientific notation form look like?

Base TenDecimal Number

Exponent1.45 x 102

Writing from standard form to scientific notation form

Number in standard form

1st Step – look where to place the decimal point. Will it go in the front of the 3 or behind the 2?

2nd Step – move decimal to the left two places.

382 382. 3.82

S.N. Rule # 1 – when moving decimals the first number in the decimal must either equal to 1, or be more than 1 but less than 10!

Writing from standard form to scientific notation form

3.82 x 102

3rd step - multiply 3.82 by base of 10.

4th step - since you move the decimal point two places to the left, the base of 10 has a power of 2.

Writing from standard form to scientific notation form

Number in standard form

Question # 2 – Which way should I move the decimal point, and where do I stop?

Answer # 1: It is a small number because the decimal is in the front.

.000525

Question # 1– Is this a big number or small number?

Answer # 2: You have to move the decimal to the right and stop after 5.

5.25

Writing from standard form to scientific notation form

5.25 x 10-4

Same steps – multiply 5.25 by the base of 10; however since you move the decimal point four places to the right and the number is below 1, the base of 10 has a negative power of 4.

Writing from standard form to scientific notation form

Practice : Write the following numbers in Scientific notatoin:

1.) 5, 185, 700

2.) 0.0000211

5.1857 x 106

2.11 x 10-5

Writing from scientific form to standard form.

Rule# 2 – When multiplying by a positive base power of 10, the decimal point moves to the right.

Write 5.36 x 105 in standard form:

5.36 536000Move decimal point 5 places to the right, 105 = 100,000

5.36 x 105 = 536000

Writing from scientific form to standard form.

Rule# 3 – When multiplying by a negative base power of 10, the decimal point moves to the left.

Write 3.24 x 10-7 in standard form:

3.24 .000000324Move decimal point 7 places to the left, 10-7 = .00000013.24 x 10-7 = .000000324

Writing from scientific form to standard form.

Practice : Write the following Scientific Notations in standard form:

a.) 7.42 x 103 =

b.) 8.83 x 10-5 =

7420

.0000883

Summary1. What are some important strategies you should

remember when writing in scientific notation?

2. What are some important factors to remember when writing from standard for to scientific notation and scientific notation to standard form?

3. Do you have clear understanding on what scientific notation is all about?

4. Are there any more questions you may have about scientific notation