Efficacy of the Scientific Notation

Examples, videos, and solutions to help Grade 8 students learn how to work with very small and very large numbers expressed in scientific notation.

New York State Common Core Math Grade 8, Module 1, Lesson 11

Worksheets for Grade 8

Lesson 11 Student Outcomes

• Students continue to practice working with very small and very large numbers expressed in scientific notation.
• Students read, write, and perform operations on numbers expressed in scientific notation.

Lesson 11 Summary

• We can read, write, and operate with numbers expressed in scientific notation.

Classwork

Exercise 1
The mass of a proton is: 0.000000000000000000001672622 kg
In scientific notation it is:

Exercise 2
The mass of an electron is: 0.0000000000000000000000910938291 kg
In scientific notation it is:

Exercise 3
Write the ratio that compares the mass of a proton to the mass of an electron.

Example 1
The advantage of the scientific notation becomes even more pronounced when we have to compute how many times heavier a proton is than an electron.

Exercise 4
Compute how many times heavier a proton is than an electron (that is, find the value of the ratio). Round your final answer to the nearest one.

Example 2
The U.S. national debt as of March 23, 2013, rounded to the nearest dollar, is $16,755,133,009,522. According to the 2012 U.S. census, there are about 313,914,040 U.S. citizens. What is each citizen’s approximate share of the debt?

Exercise 5
The geographic area of California is 163,696 sq. mi, and the geographic area of the US is 3,794,101 sq. mi. Let’s round off these figures to 1.637 x 10⁵ and 3.79x x 10⁶. In terms of area, roughly estimate how many Californias would make up one US. Then compute the answer to the nearest ones.

Exercise 6
The average distance from Earth to the moon is about 3.84 x 10⁵, and the distance from Earth to Mars is approximately 9.24 x 10⁷km in year 2014. On this simplistic level, how much further is when traveling from Earth to Mars than from Earth to the moon?

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Powers of Ten
Powers of Ten takes us on an adventure in magnitudes. Starting at a picnic by the lakeside in Chicago, this famous film transports us to the outer edges of the universe. Every ten seconds we view the starting point from ten times farther out until our own galaxy is visible only a s a speck of light among many others. Returning to Earth with breathtaking speed, we move inward- into the hand of the sleeping picnicker- with ten times more magnification every ten seconds. Our journey ends inside a proton of a carbon atom within a DNA molecule in a white blood cell.

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Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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