PRACTICE: Scientific notation word problems
[CHALLENGE LEVEL]
CALCULATOR NOTE:

Get into the habit of putting parentheses around numbers in scientific notation
when you use your calculator. Otherwise, you can run into problems.

For example, say you wanted to divide 1.5 × 1011 by 3 × 108.
If you don’t use parentheses, your calculator will use order of operations and
multiply 1.5 by 1011 and then divide that by 3 and then multiply the result by 108.
You won’t be dividing by 3 × 108. You’ll just be dividing by 3.
Using (1.5 × 1011)  (3 × 108) gets you the answer you want.
1) The speed of light is approximately 3 × 108 meters per second. The Earth is
about 1.5 × 1011 meters from the sun.
a. How many seconds does it take light to travel from the sun to the
Earth?
b. To the nearest minute, how many minutes is that?
2) The Earth has a mass of 5.97 × 1024 kg, while the moon has a mass of
7.35 × 1022 kg.
a. How many kilograms heavier is the Earth than the moon?
b. To the nearest whole number, how many times greater is the mass of
the Earth than the mass of the moon?
3) Scientists generally believe the Earth is 4.543 billion years old and that the
dinosaurs went extinct 65.5 million years ago.
a. Use standard notation to express this age of the Earth in years. Then
convert this to scientific notation.
b. Use standard notation to express the number of years ago the
dinosaurs went extinct. Then convert this to scientific notation.
c. How many years older is the Earth than the last of the dinosaurs?
D. Stark 11/22/2016
4) In 1950, the world’s population was 2.556 billion people. As of 2013, it was
7.125 billion.
a. How many more people lived in 2013 than in 1950? Express your
answer in scientific notation.
b. To the nearest percent, what’s the percent increase in world
population from 1950 to 2013?
5) A red blood cell is 8 millionths of a meter long.
a. Express this size in standard notation.
b. Express this size in scientific notation.
c. If you could place 1250 such cells directly next to one another along a
straight line, how long would the line be in centimeters?
6) In 2012 there were approximately 314.1 million Americans. In that year
Americans ate nearly 50 billion burgers.
a. Express this number of people in scientific notation.
b. Express this number of burgers in scientific notation.
c. To the nearest burger, how many burgers per person was that for
2012?
d. To the nearest burger, how many burgers would that be per week?
e. Assuming each hamburger is a quarter-pounder, how many pounds of
burger did Americans eat overall in 2012?
D. Stark 11/22/2016
PRACTICE: Scientific notation word problems
KEY
[CHALLENGE LEVEL]
1) The speed of light is approximately 3 × 108 meters per second. The Earth is
about 1.5 × 1011 meters from the sun.
a. How many seconds does it take light to travel from the sun to the
Earth?
b. To the nearest minute, how many minutes is that?
2) The Earth has a mass of 5.97 × 1024 kg, while the moon has a mass of
7.35 × 1022 kg.
a. How many kilograms heavier is the Earth than the moon?
D. Stark 11/22/2016
b. To the nearest whole number, how many times greater is the mass of
the Earth than the mass of the moon?
3) Scientists generally believe the Earth is 4.543 billion years old and that the
dinosaurs went extinct 65.5 million years ago.
a. Use standard notation to express this age of the Earth in years. Then
convert this to scientific notation.
b. Use standard notation to express the number of years ago the
dinosaurs went extinct. Then convert this to scientific notation.
c. How many years older is the Earth than the last of the dinosaurs?
D. Stark 11/22/2016
4) In 1950, the world’s population was 2.556 billion people. As of 2013, it was
7.125 billion.
a. How many more people lived in 2013 than in 1950? Express your
answer in scientific notation.
b. To the nearest percent, what’s the percent increase in world
population from 1950 to 2013?
D. Stark 11/22/2016
5) A red blood cell is 8 millionths of a meter long.
a. Express this size in standard notation.
b. Express this size in scientific notation.
c. If you could place 1250 such cells directly next to one another along a
straight line, how long would the line be in centimeters?
6) In 2012 there were approximately 314.1 million Americans. In that year
Americans ate nearly 50 billion burgers.
a. Express this number of people in scientific notation.
b. Express this number of burgers in scientific notation.
D. Stark 11/22/2016
c. To the nearest burger, how many burgers per person was that for
2012?
d. To the nearest burger, how many burgers would that be per week?
e. Assuming each hamburger is a quarter-pounder, how many pounds of
burger did Americans eat overall in 2012?
D. Stark 11/22/2016