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Illustrative Math
Grade 8
Let’s use powers of 10 to help us make calculations with large and small numbers.
Illustrative Math Unit 8.7, Lesson 12 (printable worksheets)
Powers of 10 can be helpful for making calculations with large or small numbers. For example, in 2014, the United States had 318,586,495 people who used the equivalent of 2,203,799,778,107 kilograms of oil in energy. The amount of energy per person is the total energy divided by the total number of people.
We can use powers of 10 to estimate the total energy as 2 · 1012 and the population as 3 · 108.
So the amount of energy per person in the U.S. is roughly (2 · 1012) ÷ (3 · 108)
That is the equivalent of 2/3 · 104 kilograms of oil in energy. That’s a lot of energy—the equivalent of almost 7,000 kilograms of oil per person!
In general, when we want to perform arithmetic with very large or small quantities, estimating with powers of 10 and using exponent rules can help simplify the process. If we wanted to find the exact quotient of 2,203,799,778,107 by 318,586,495, then using powers of 10 would not simplify the calculation.
What information would you need to answer the following questions?
Here is a problem that will take multiple steps to solve. You may not know all the facts you need to solve the problem. That is okay. Take a guess at reasonable answers to anything you don’t know. Your final answer will be an estimate.
If everyone alive on Earth right now stood very close together, how much area would they take up?
In 2016, the Burj Khalifa was the tallest building in the world. It was very expensive to build.
Consider the following question: Which is taller, the Burj Khalifa or a stack of the money it cost to build the Burj Khalifa?
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