Lesson 1-9: Scientific Notation

ObjectivesStudents will be able to write numbers as

scientific notation as well as perform operations with scientific notation.

Warm-up 1-9

31

0.54

1000000

0.0001

109

1012

1071

Scientific Notation

a • 10n , where 1 < a < 10 and n is an integer

Allows us to write the mass of the earth: 5,974,000,000,000,000,000,000,000 kg

as5.974 • 1024

Remember:

Large numbers: 10positive

Small numbers: 10negative

Exponent tells you how far to move the decimal!

Express each number in standard notation.

a.

b.

Answer: 0.0316

Answer: 7610

In-Class Example #1

Operations with Scientific NotationKeep the parts separate and adjust when finished:1) Multiply/Divide “a” numbers2) Use properties of exponents to evaluate powers of 103) Adjust final scientific notation:

1) If you have to make the “a” number smaller, the you make the exponent bigger by the same number of decimal places

2) If you have to make the “a” number bigger, you make the exponent smaller by the same number of decimal places

In-Class Example 2 45 102.4106.3 91012.15 1010512.1

10

4

106.8

1042.3 61040.0 7100.4