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)