1.2: Millions, Billions, or Trillions?

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INTRODUCTION

Take a moment to discuss the following questions in your group:

How big is a million? A trillion? A billion? Can you think of any good ways to describe these amounts?
How can you compare them?
Can you think of an example of using each in real life?

SPECIFIC OBJECTIVES

By the end of this collaboration, you should understand that

keeping track of the number of decimal places in large numbers is useful for rough estimations.
there are huge differences between measures of a million, a billion, and a trillion.

By the end of this collaboration, you should be able to

estimate the approximate size of the product of several large quantities.

PROBLEM SITUATION: HOW MUCH IS A TRILLION?

In the following questions, you will be presented with various situations. After reading the situation, consider your own estimation strategies before sharing your ideas in your group.

(1) Fill in the table below by describing your estimation strategy for each situation. Include your final estimated quantity. Write if your estimated quantity is in the millions, billions, trillions or some other size, such as tens of millions.

Quantity	Describe your strategy and explain your estimate
(a) In 2020, there were about 1.1 million working people in the U.S. who made at or below the federal minimum wage of $7.25 per hour. Estimate the amount of money needed per year to raise wages to $15 per hour. Hint: Assume a person works 40 hours per week for 52 weeks a year.
(b) Estimate the amount of money needed to buy everyone in the United States a box of Girl Scout cookies. Hint: Assume a box of cookies cost $5 and the population of the U.S. is about 334 million.
(c) Estimate the amount of money needed to pay for public college tuition and fees for four years. In 2021, there were approximately 14.63 million college students in the U.S. The average cost of college per year was about $25 thousand.
(d) If the U.S. national debt was $30 trillion in March of 2022 and was evenly divided among people living in the United States, estimate how much each person’s share would be. Hint: The population of the U.S. was about 334 million in 2022.

(2) Now, use a calculator to refine your estimates.

Quantity	Calculated Amount
(a) In 2020, there were about 1.1 million working people in the U.S. who made at or below the federal minimum wage of $7.25 per hour. Calculate the amount of money needed per year to raise wages to $15 per hour. Hint: Assume a person works 40 hours per week for 52 weeks a year.
(b) Calculate the amount of money needed to buy everyone in the United States a box of Girl Scout cookies. Hint: Assume a box of cookies cost $5 and the population of the U.S. is about 334 million.
(c) Calculate the amount of money needed to pay for students to attend the University System of Ohio for four years. In 2020, the total students enrolled in this system was about 526 thousand, and tuition and fees were about $13,000 per year.

(3) In Question 2 above, we tried to find more precise quantities. Why are the results still referred to as estimates?

(4) (a) If the U.S. budget was about $6.011 trillion in 2022, estimate the percentage of the budget which would be needed to pay for your estimate in Question 1a, rounded to $18 billion, for raising the minimum wage to $15 per hour. Round to the nearest tenth of a percent.

(b) If the U.S. budget is about $3.8 trillion, calculate the percentage of the budget which would be needed to pay or your calculation in Question 2a above, for raising the minimum wage. Round to the nearest hundredth of a percent.

MAKING CONNECTIONS

Record the important mathematical ideas from the discussion.

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