Aim how can we express very large and very small numbers easily
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Aim: How can we express very large and very small numbers easily?. Do Now Choose one: Express 534 megameters in meters Describe in full sentences the method for converting between unit prefixes (for example grams to kilograms). Big and small numbers.

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Aim: How can we express very large and very small numbers easily?

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Aim how can we express very large and very small numbers easily

Aim: How can we express very large and very small numbers easily?

Do Now

Choose one:

Express 534 megameters in meters

Describe in full sentences the method for converting between unit prefixes (for example grams to kilograms)


Big and small numbers

Big and small numbers

  • Do you know this number: 300,000,000 m/sec?

  • It’s the speed of light!

  • What about 0.00000000000000000000000000167 kg?

  • It’s the mass of a single proton.


Scientific notation

Scientific Notation

  • Just like a standard system of units makes measuring easier, using a standard system to express large and small numbers makes doing calculations easier.

  • We call this system Scientific Notation.


Scientific notation1

Scientific Notation

  • Scientific Notation involves using powers of ten to represent the excess zeros.

  • Move the decimal all the way so it is behind the first significant digit

  • So the speed of light (300,000,000 m/s) is written as 3.0 x 108 m/s


Scientific notation rules

Scientific Notation Rules

  • For large numbers, put the decimal after the first digit. That will be your coefficient.

  • For example 123,000,000,000

  • Count how many places you had to move the decimal. That will be your power of 10.

  • We also call this the order of magnitude.

  • Write it in Scientific Notation form: 1.23 x 1011


Scientific notation rules1

Scientific Notation Rules

  • For small numbers, put the decimal behind the first non-zero digit in the decimal.

  • Again, count how many spaces you moved the decimal. That is your negative exponent or order of magnitude.

  • For example: .00000000139 is 1.39 x 10-9


Practice problems try on your own

Practice problems – Try on your own

0.0000514 =

1,630,000 =


Math with scientific notation

Math with Scientific Notation

  • When multiplying numbers in Scientific Notation: Multiply the coefficients (front numbers), keep the 10 and add the exponents.

  • 4.0 x 105 * 2.0 x 106 = ???

  • When dividing numbers in Scientific Notation: Divide the coefficients (front numbers), keep the 10 and subtract the exponents.

  • 4.0 x 105/ 2.0 x 106 = ???


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