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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