Day 3 –Adding and Subtracting Numbers in Scientific Notation
Example 1 - Subtracting
The population of New York State is approximately 1.96 x 107. The
population of New York City alone is 8,245,000. How many people do not
live in New York City?
To find the number of people that live in New York State but not in New York City, we must
the population of
from the population of
_
First, we need to change the population of New York City to scientific notation.
To find the difference, we subtract:
To find the difference (or sum) of numbers in scientific notation, it is best to make the order
of magnitude (n) the same in all numbers.
Therefore, each number must have the same base (10) and same order of magnitude (n).
We can rewrite the population of New York State as an integer multiplied by 106 and then
subtract.
Example 2 - Subtracting
The approximate thickness of an iPhone 4s is 9.398 x 10-1 centimeters. The approximate
thickness of a standard deck of 52 cards is 1.515 x 100. Which is thicker? Justify your
answer.
What is the difference between the thickness of an iPhone 4s and a standard deck of
52 cards?
Practice 1
a) According to scientists, the Earth’s mass is 5.98 x 1024 kilograms. The mass of
the Sun is 1.989 x 1030. How much greater is the mass of the Sun than the
mass of the Earth?
b) A quarter is approximately 0.07 inches thick. A dollar bill is approximately 4.3 x
10-3 inches thick. Using scientific notation, determine which piece of money is
thicker and by how much.
Example 3 – Adding
The approximate area of the Pacific Ocean is 6.4 x 107 square smiles. The approximate area
of the Arctic Ocean is about 5.4 x 106 square miles.
1. Find the approximate sum of the areas of the two oceans.
a. Rewrite the area of the Pacific Ocean to have the same order of magnitude as the
Arctic Ocean.
b. Can we find the same answer by rewriting the area of the Arctic Ocean to have the
same order of magnitude as the Pacific Ocean? Justify your reasoning.
2. About how much larger is the area of the Pacific Ocean than the Arctic Ocean?
Partner Practice
a) (1.2 x 105) + (5.35 x 106)
e) (8.41 x 10-5) – (7.9 x 10-6)
b) (6.91 x 10-2) + (2.4 x 10-3)
f) (1.33 x 105) – (4.9 x 104)
c) (9.70 x 106) + (8.3 x 107)
g) (1.5 x 107) – (8.9 x 105)
d) (3.67 x 102) – (1.6 x 101)
h) (2.45 x 103) + (1.23 x 101)