Scientific Notation Word Problems
1) According to scientists, the Earth’s mass is 5.98 x 1024
kilograms. The mass of the Sun is 1.989 x 1030 kilograms.
How much greater is the mass of the Sun than the mass of
the Earth?
Explanation:
- First we write the mass of the Sun as 1.989 x 1030 and the
mass of Earth as 5.98 x 1024.
- We have to subtract 5.98 x 1024 from 1.989 x 1030
1.989 x 1030 – 5.98 x 1024
(Remember what we do when we subtract in scientific
notation)
 Choose the highest exponent. Take the difference.
Convert the constant of the lower exponent.
Move 5.98 to the LEFT 6 places. = 0.00000598
1.98 – 0.00000598= 1.98899402 x 1030
So the answer is 1.98899402 x 1030.
2) Last year, we noticed the population of Tamworth was
5.6 x 103. The population of Liverpool was 1.3 x 104. Which
town had a larger population and by how much?
Explanation:
- First we write the population of Liverpool, 1.3 x 104,and
the population of Tamworth, 5.6 x 103.
- We can see the Liverpool is set to the higher power of ten
and is, thus, the larger town.
- To find the increased population we have to subtract the
population of Tamworth from Liverpool
= 1.3 x 104 – 5.6 x 103
- Get them into the same power of ten to make it workable.
= 5.6 becomes .56
- Put the constants together.
(1.3 - .56)= 0.74
- Final Answer: 0.74 x 104
3) In Russia, the population was 290.9 million people in 2002.
The total health care costs for the country at that time
were $1.7 trillion. Calculate the average amount spent per
person on health care cost.