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# Scientific Notation - PowerPoint PPT Presentation

Scientific Notation. Scientific Notation – Justification. Scientists often work with very large and very small numbers, however these can be cumbersome to work with. To simplify matters we write these numbers using exponents or scientific notation. . Scientific Notation – Broken Down.

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Presentation Transcript

• Scientists often work with very large and very small numbers, however these can be cumbersome to work with. To simplify matters we write these numbers using exponents or scientific notation.

• The number 123 000 000 000 in scientific notation is written as: ______________________

• Coefficient: this is the first number, 1.23; it must be ____________________________________________

• Base: this is the second number, 10; in scientific notation it must ______________________________

• Exponent: this is the third number, 11; this must always be an _________________

• It can be positive when expressing a ___________________

• i.e.: 123 000 000 000 = 1.23 x 1011

• It can be negative when expressing a ___________________

• i.e.: 0.0000603 = 6.03 x 10-5

• 1. Large numbers - 36000 written in scientific notation is 3.6 x 104. Count the number of decimal places you move to the _______and this becomes the exponent.

• 2. Small numbers - 0.00015 written in scientific notation is 1.5 x 10-4 . Notice that a negative exponent is used when moving the decimal to the ________

• Rule of ThumbWhen you make the number smaller, make the exponent ___________and when you make the number larger, make the exponent ____________

• Scenario 1: Like Exponents

• Add or subtract the numerical coefficient and keep the exponent the same. If the numerical coefficient becomes higher than 10 or lower than 1, adjust the exponent.

• Example:

• ____________________________________________________

• Scenario 2: Unlike Exponents

• Change one of the exponents (usually make the smaller one larger) so both exponents are the same, then add or subtract the numerical values.

• Example:

• ________________________________________

• ________________________________________

• ________________________________________

• Quantities do not need the exponents to be the same when multiplying or dividing.

• Multiplying: Multiply the numerical coefficients and add the exponents. Don't forget to multiply the units.

• Example:

• _________________________________________________

• Dividing: Divide the numerical coefficients and subtract the exponents. Remember to divide the units.

• Example:

• _________________________________________________