Scientific Notation for Easy Numbers

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Scientific Notation for Easy Numbers
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Todays Learning Goals

• We will begin to understand how to write some
  numbers using scientific notation.

• We will learn to use base-10 factorizations as
  part of our scientific notation.

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Base-10 Factorizations

• Previously, we discussed how to factor powers of
  10 using base-10 factorizations. For example,
  what is the base-10 factorization for 1000?

1000
Yes1000 103.

• How could we have just looked at the number 1000
  and known that it was 103?

Awesome1000 has 3 zeros in it. So, the base-10
factorization has an exponent of 3. Thus, 1000
103.
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Base-10 Factorizations

• What are the base-10 factorizations for the
  following numbers?

a) 10
b) 10,000
c) 100,000,000
10 101
10,000 104
100,000,000 108
d) 1
e) 100,000
f) 1,000,000
1 100
100,000 105
1,000,000 106
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Scientific Notation

• Because we use a base-10 system, every number can
  be written as a multiple of a power of 10.

300

• For example, the number 300 is the same as 3100.
  To write the number 300 in scientific notation,
  we would write 3102.

300 3102

• Scientific Notation is a way to write any number
  (particularly very large or very small numbers)
  using the fact that they are multiples of powers
  of 10.

• Scientific Notation has the following form
• A number between 1 and 10 base-10
  factorization

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Scientific Notation

• How would you write the following numbers using
  scientific notation?

a) 500
b) 20,000
c) 4,000,000,000
5100 5102
210,000 2104
41,000,000,000 4109

• Notice how scientific notation is a shorter way
  to write large numbers like 4,000,000,000. This
  is why scientists developed scientific notation!

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Scientific Notation

• Using our calculators, multiply
  2,000,0002,000,000. What does the calculator
  give you as an answer?

Yes4E12.

• What do you think 4E12 means?

Nice4E12 41012.

• So, what is the answer to 2,000,0002,000,000 if
  we wrote the answer out in standard form?

Great4E12 is 4 with 12 zeros
4,000,000,000,000.
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Partner Work

• You have 20 minutes to work on the following
  problems with your partner.

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For those that finish early

• 1. Write the number for 51021 out long hand.
• 2. Write the following numbers using scientific
  notation.
• a) 4 b) 0 c) 40

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Big Idea from Todays Lesson

• Scientific Notation has the following form
• A number between 1 and 10 base-10
  factorization
• Scientific Notation is a short-hand way to write
  large numbers.
• In our calculators, the E stands for scientific
  notation.
• For example 9 E 12 means 91012

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Homework

• Complete Worksheet.