Scientific Notation Word Problems

This lesson is about six carefully chosen scientific notation word problems along with their solutions.

Example #1:

Jupiter is the largest planet in our solar system and its mass in scientific notation is about 1.9 × 10²⁷. Write the mass in standard notation.

Solution:

1.9 × 10²⁷ = 1.9 × 10 × 10²⁶ = 19 × 10²⁶ = 1900000000000000000000000000

The mass of Jupiter in standard notation is 1900000000000000000000000000

Example #2:

It is predicted that the world population in 2025 may reach eight billion. Write eight billion in scientific notation.

Solution:

Eight billion = 8000000000 = 8 × 10⁹

Example #3:

The oxygen atom has a mass of about 0.00000000000000000000000003 kg. Write the mass of the oxygen atom in scientific notation.

Solution:

0.00000000000000000000000003 = 3 × 10^-26 kg

Example #4:

The following masses which are parts of an atom are measured in grams. Order the parts of an atom from greatest to least mass. 

electron: 9.1096 × 10^-28, neutron: 1.6749 × 10^-24, proton: 1.6726 × 10^-24

Solution:

The smallest mass is since 9.1096 × 10^-28 since -28 will create more zeros after the decimal point.

1.6749 × 10^-24 and 1.6726 × 10^-24 have the same exponent. So we just need to compare 1.6749 to 1.6726.

Since 1.6726 is smaller than 1.6749, 1.6726 × 10^-24  is smaller than 1.6749 × 10^-24

From greatest to least mass, we get: 1.6749 × 10^-24 > 1.6726 × 10^-24 > 9.1096 × 10^-28 

Example #5:

The weight of an adult male elephant is about 5600 kg. What is the weight in scientific notation?

Solution:

In scientific notation the weight of an adult male elephant is 5.6 × 10³

Example #6:

A computer can perform about 5 × 10⁸ instructions per second. How many instructions is that per hour? Express the answer in scientific notation.

Solution:

1 hour is equal to 3600 seconds. Therefore, we need to multiply 5 × 10⁸ by 3600

3600 × 5 × 10⁸ = 36 × 10² × 5 × 10⁸

3600 × 5 × 10⁸ = 36 × 5 × 10² × 10⁸

3600 × 5 × 10⁸ = 180 × 10¹⁰

3600 × 5 × 10⁸ = 1.80 × 10¹²

3600 × 5 × 10⁸ = 1.8 × 10¹²

The computer can perform about 1.8 × 10¹² instructions per hour