Estimating Quantities

Examples, videos, and solutions to help Grade 8 students learn how to compare and estimate quantities in the form of a single digit times a power of 10.

New York State Common Core Math Grade 8, Module 1, Lesson 8

Worksheets for Grade 8

Lesson 8 Student Outcomes

• Students compare and estimate quantities in the form of a single digit times a power of 10.
• Students use their knowledge of ratios, fractions, and laws of exponents to simplify expressions.

Lesson 8 Summary

• In general, close approximation of quantities will lead to more precise answers.
  
• We can multiply and divide numbers that are written in the form of a single-digit integer times a power of 10.

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Classwork
Example 1:
In 1723, the population of New York City was about 7,248. By 1870, almost 150 years later, the population had grown to 942,292. We want to determine approximately how many times greater the population was in 1870, compared to 1723.

Exercise 1:
The Federal Reserve states that the average household in January of 2013 had $7,122 in credit card debt. About how many times greater is the US national debt, which is $16,755,133,009,522? Rewrite each number to the nearest power of 10 that exceeds it, and then compare.

Example 2:
Let’s compare the population of New York City to the population of New York State. Specifically, let’s find out how many times greater the population of New York State is compared to that of New York City.

Example 3:
There are about 9 billion devices connected to the Internet. If a wireless router can support 300 devices, how many wireless routers are necessary to connect all 9 billion devices wirelessly?

Exercise 2:
There are about 3,000,000 students attending school, kindergarten through 12th grade, in New York. Express the number of students as a single-digit integer times a power of 10.
The average number of students attending a middle school in New York is 8 x 10². How many times greater is the overall number of K-12 students compared to the number of middle school students?

Exercise 3:
A conservative estimate of the number of stars in the universe is 6 x 10²². The average human can see about 3,000 stars at night with his naked eye. About how many times more stars are there in the universe, compared to the stars a human can actually see?

Exercise 4:
The estimated world population in 2011 was 7 x 10⁹. Of the total population, 682 million of those people were left- handed. Approximately what percentage of the world population is left-handed according to the 2011 estimation?

Example 4:
The average American household spends about $40,000 each year. If there are about 1 x 10⁸ households, what is the total amount of money spent by American households in one year?

Exercise 5
The average person takes about 30,000 breaths per day. Express this number as a single-digit integer times a power of 10.
If the average American lives about 80 years (or about 30,000 days), how many total breaths will a person take in her lifetime?

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