Multiplying and Dividing by Powers of 10; Scientific Notation Section 4.5

Objectives Multiply or divide a number of by a power of 10 Write a number in scientific notation or change a number in scientific notation to a place value name

Objective 1: Multiply or divide a number of by a power of 10

Objective 1 Power of 10 – value when 10 is raised to a power (exponent) Multiplying Multiplying by 10 moves the decimal point one place to the right Multiplying by 100, which is 10², move decimal point two places to the right Etc. Write zeros on the right to ensure correct number of decimal places

Objective 1 Dividing Move decimal point to the left Write zeros on the left to ensure correct number of decimal places

Objective 2: Write a number in scientific notation or change a number in scientific notation to place value name

Objective 2 Scientific notation – way to write numbers as a product using a number between 1 and 10 times a power of 10 Used to write very large or very small numbers Mass of earth: 6,000,000,000,000,000,000,000,000 kg = 6.0 x 1024 kg Mass of a hydrogen atom: 0.0000000000000000000000017 g = 1.7 x 10-24 grams

Objective 2 To write a number in scientific notation Move decimal point left or right so only one digit (between 1 and 9) is to the left of decimal Multiply the number by a power of 10. The exponent will be the number of moves to the left or right If it was a large number and you moved decimal to the left, the exponent is positive If it was a small number and you moved decimal to the right, the exponent is negative

Objective 2 To change from scientific notation to place value name If exponent is positive, move decimal to the right as many times as the exponent (make a big number) If the exponent is negative, move decimal to the left (make a small number)