10.6 Standard form to Scientific Notation Essential Question: How can you write numbers in scientific notation?

REVIEW 1.79 x 10 standard form=written as normal # ex. 5,400 scientific notation # written as two factors using power of 10 standard form=written as normal # ex. 5,400 4 1.79 x 10 A power of 10 1-9 in front of decimal

RULES – Standard Form Scientific Notation 1. Always start at the DECIMAL (or imaginary decimal ex. 5 is 5.0) 2. Make scoops from the decimal & Stop when there is only a digit of 1-9 to the left of decimal (Value of factor 𝟏 ≥ # <𝟏𝟎) 3. COUNT the SCOOPS- this is your exponent 4. A standard form # less than one, will have a negative exponent 5. A standard form # greater than 9 will have a positive exponent When moving decimal LEFT then ADD to exponent, When moving decimal RIGHT, subtract from exponent

Left Add Right Subtract Standard Form Scientific Notation HINT!! When moving decimal LEFT then ADD to exponent, When moving decimal RIGHT, subtract from exponent LARS from Mars: Left Add Right Subtract

RULES – Standard Form Scientific Notation Always start at the DECIMAL (or imaginary decimal ex. 5 is 5.0) 2. Stop when there is only one number of 1-9 to the left of decimal 3. Count the scoops, NOT the zeros, this is your exponent 4. A standard form # less than one, will have a negative exponent 5. A standard form # greater than 9 will have a positive exponent

Example 1: Write the number in scientific notation 57,000 6830 25,000,000 0.00033 0.000506 0.007

Example 2 Google purchased YouTube for $1,650,000,000 Write this number in scientific notation. Example 3 The 2004 Indonesian earthquake slowed the rotation of the Earth, making the length of a day 0.00000268 second shorter. Write this number in scientific notation.

In scientific notation, each cable can hold 3.0  105 pounds. An oil rig can hoist 2,400,000 pounds with its main derrick. It distributes the weight evenly between 8 wire cables. What is the weight that each wire cable can hold? Write the answer in scientific notation. Find the weight each cable is expected to hold by dividing the total weight by the number of cables. 2,400,000 pounds ÷ 8 cables = 300,000 pounds per cable Each cable can hold 300,000 pounds. Now write 300,000 pounds in scientific notation. 3.0  10 In scientific notation, each cable can hold 3.0  105 pounds.