Intro to Scientific Notation
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Common Core Standard: Use numbers expressed in the form of a single digit times an integer power of 10 to
estimate very large or very small quantities, and to express how many times as much one is than the other.
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Scientific Notation is used to write really big or really small numbers
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As the name suggests scientific notation is often used in science!
Scientific Notation is written in two parts
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First part is written as a single digit followed by a decimal point
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Second part is written as ten to a power
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The power is how many times the decimal point is moved
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A positive exponent is for a big number
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A negative exponent is for a small number
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Pictures:
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Example: Write 3.4 x 105 in standard form
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3.4 x 105 , has a positive exponent, so it is a big number
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The exponent indicates that the decimal needs to move five times to make it bigger
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= 340,000
Example: 4.65 x 10-8 in standard form
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4.65 x 10-8, has a negative exponent, so it is a small number
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The exponent indicates that the decimal needs to move eight times to make it smaller
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= 0.0000000465
Example: Write 25,000 in scientific notation
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Needs to be a single digit, so move decimal point between the 2 and 5
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This would move the decimal point 4 times
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Since it is a big number the exponent must be positive
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2.5 x 104
8
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Estimation Example: The population of the US is about 3 x 10 million. The population of the world is about 7 x 10
million. Estimate about how many times bigger the world population is than the US’s population.
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Seven is about twice as big as 3
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The US is one exponent smaller than world
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Thus, the US’s population is about 20 times smaller than the world’s population