Scientific Notation

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Scientific Notation

• A number is expressed in scientific notation when
  it is written as the product of a number and a
  power of ten.
• The number must be greater than or equal to 1 and
  less than 10.

Number greater than or equal to 1, but less than
10
Power of 10 written in exponential form
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The Distance From the Sun to the Earth
93,000,000
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Step 1

• Move decimal to the left
• Leave only ONE number in front of decimal

93,000,000 --gt 9.3000000
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Step 2

• Write number without zeros

9.3000000 9.3
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Step 3

• Count how many places you moved the decimal
• Make that your exponent

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Practice Problems
Write in scientific notation. Decide the
exponent.

1. 98,500,000 9.85 x 10?
2. 64,100,000,000 6.41 x 10?
3. 279,000,000 2.79 x 10?
4. 420,000 4.2 x 10?

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Standard form is the opposite of scientific
notation

• To write in standard form, move the decimal the
  same number of places as the exponent.
• The sign of the exponent tells which direction to
  move the decimal. A positive exponent means move
  the decimal to the right.

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More Practice Problems
Write in standard form

1. 7.34 x 108
2. 8.7 x 103
3. 9 x 105

Answers

1. 734,000,000

3) 900,000
2) 8,700
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Lets get started on the homework

• W.S. 3-7 Front AND back
• Remember to be quiet!!

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Warm-Up

• Write in scientific notation
• 1.) 2,000,000,000
• 2.) 36,500,000
• 3.) 465,000,000,000,000
• Write in standard form
• 4.) 4.62 x 105
• 5.) 3 x 103

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What if your number is a decimal?

• Step 1

• Move decimal to the right
• Leave only one number in front of decimal

0.0000896 --gt 00008.96
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Step 2

• Write number without zeros

000008.96 8.96
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Step 3

• Count how many places you moved the decimal
• Make that your exponent
• Since your number was a decimal to begin with the
  power is a negative!

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Practice Problems
Write in scientific notation. Decide the power
of ten.

1. 0.00000658 6.58 x 10?
2. 0.000000000641 6.41 x 10?
3. 0.0000000123 1.23 x 10?
4. 0.0000068 6.8 x 10?

15
Standard form is the opposite of scientific
notation

• To write in standard form, move the decimal the
  same number of places as the exponent.
• The sign of the exponent tells which direction to
  move the decimal. A positive exponent means move
  the decimal to the right, and a negative exponent
  means move the decimal to the left.

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More Practice Problems
Write in standard form

1. 4.35 x 10-8
2. 8.7 x 10-6
3. 5.2 x 10-5

Answers

1. 0.0000000435

2) 0.0000087
3) 0.000052