Lesson 12: Practice Problems

Problem 1

Which is larger: the number of meters across the Milky Way, or the number of cells in all humans? Explain or show your reasoning.

Some useful information:

The Milky Way is about 100,000 light years across.
There are about 37 trillion cells in a human body.
One light year is about $10^{16}$ meters.
The world population is about 7 billion.

Problem 2

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 3

Perform the following calculations. Express your answers in scientific notation.

$(2 \times 10^{5}) + (6 \times 10^{5})$
$(4.1 \times 10^{7}) \cdot 2$
$(1.5 \times 10^{11}) \cdot 3$
${(3 \times 10^{3})}^{2}$
$(9 \times 10^{6}) \cdot (3 \times 10^{6})$

Problem 4

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 5

Diego was solving an equation, but when he checked his answer, he saw his solution was incorrect. He knows he made a mistake, but he can’t find it. Where is Diego’s mistake and what is the solution to the equation?

$\begin{array}{r} - 4 (7 - 2 x) = 3 (x + 4) \\ - 28 - 8 x = 3 x + 12 \\ - 28 = 11 x + 12 \\ - 40 = 11 x \\ - \frac{40}{11} = x \end{array}$

Problem 6 From Unit 5 Lesson 13

Here is the graph for one equation in a system of equations.

A graph showing a line crossing the x axis at (2, 0) and the y axis at (0, -3)

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 $(4, 3)$ .