Lesson 13
Definition of Scientific Notation
Let’s use scientific notation to describe large and small numbers.
Problem 1
Write each number in scientific notation.
 14,700
 0.00083
 760,000,000
 0.038
 0.38
 3.8
 3,800,000,000,000
 0.0000000009
Problem 2
Perform the following calculations. Express your answers in scientific notation.

\((2 \times 10^5) + (6 \times 10^5)\)

\((4.1 \times 10^7) \boldcdot 2\)

\((1.5 \times 10^{11}) \boldcdot 3\)

\((3 \times 10^3)^2\)
 \((9 \times 10^6) \boldcdot (3 \times 10^6)\)
Problem 3
Jada is making a scale model of the solar system. The distance from Earth to the Moon is about \(2.389 \times 10^5\) miles. The distance from Earth to the Sun is about \(9.296 \times 10^7\) miles. She decides to put Earth on one corner of her dresser and the Moon on another corner, about a foot away. Where should she put the sun?
 On a windowsill in the same room?
 In her kitchen, which is down the hallway?
 A city block away?
Explain your reasoning.
Problem 4
Here is the graph for one equation in a system of equations.
 Write a second equation for the system so it has infinitely many solutions.
 Write a second equation whose graph goes through \((0,2)\) so that the system has no solutions.
 Write a second equation whose graph goes through \((2,2)\) so that the system has one solution at \((4,3)\).