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 × 10^{27}. Write the mass in standard notation.
Solution:
1.9 × 10^{27} = 1.9 × 10 × 10^{26} = 19 × 10^{26} = 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 × 10^{9}
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 × 10^{3}
Example #6:
A computer can perform about 5 × 10^{8} 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 × 10^{8} by 3600
3600 × 5 × 10^{8} = 36 × 10^{2} × 5 × 10^{8}
3600 × 5 × 10^{8 }= 36 × 5 × 10^{2} × 10^{8}
3600 × 5 × 10^{8 }= 180 × 10^{10}
3600 × 5 × 10^{8 }= 1.80 × 10^{12}
3600 × 5 × 10^{8 }= 1.8 × 10^{12}
The computer can perform about 1.8 × 10^{12} instructions per hour
Mar 29, 23 10:19 AM
Mar 15, 23 07:45 AM