Module 3 Lesson 2: Base 10 and Scientific Notation

Scientific Notation is a way to write numbers (usually used with incredibly large or

incredibly small numbers) as a product.

The requirements to write scientific notation: 𝑑 ∙ 10𝑛

0 < 𝑑 < 10 (note that d cannot be either 0 or 10)

𝑛 is called the order of magnitude, it can be either positive or negative and

tells how many decimal places are used.

Examples: Write each number in scientific notation

234,000 0.0035 532,100,000 0.0000000012

3.331 532,000,000 0.0000000000000000123 (there are 16 zeros)

Arithmetic Operations with Numbers Written in Scientific Notation

Addition and Subtraction: The exponent on the power of 10 must be the same.

(3.1 × 104) + (1.2 × 104) (2.6 × 1034) − (1.1 × 1034)

(2.4 × 1020) + (4.5 × 1021) (3.7 × 1034) − (1.1 × 1033)

Multiplication and Division: The exponents can be different.

(7 × 10−9)(5 × 105) (4.1 × 103)(5.2 × 102)

1.2×1015

3×107

7.5×103

1.5×1014

Application Example

The average distance between the sun and Earth is 151,268,468 km. The average

distance between the sun and Jupiter is 780,179,470 km. The average distance

between the sun and Pluto is 5,908,039,124 km.

a. What is the approximate distance from the sun to Earth (in scientific

notation)? From the sun to Jupiter? From the sun to Pluto?

b. How much farther is Jupiter from the sun than Earth is from the sun?

c. How much farther is Pluto from the sun than Jupiter is from the sun?

d. Order the distances given in the instructions from smallest to largest. How

does writing them in scientific notation help us to compare and order them?