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

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Common Core For Grade 8

• 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 10^{5} and 3.79x x 10^{6}. 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 10^{5}, and the distance from Earth to Mars is
approximately 9.24 x 10^{7}km in year 2014. On this simplistic level, how much further is when traveling from Earth to
Mars than from Earth to the moon?

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.