Name: __________________________
Multiplying and Dividing Numbers Written in Scientific Notation
Standard
notation
Scientific
notation
20
x
300
=
6,000
2.0 x 101
x
3.0 x 102
=
6.0 x 103
1. Complete the following table below. The first row represents multiplication of
numbers written in standard notation. The second row represents multiplication
of numbers written in scientific notation.
Standard
notation
Scientific
notation
Standard
notation
Scientific
notation
Standard
notation
Scientific
notation
Standard
notation
Scientific
notation
25
x
100
=
x
=
x
=
2,500
2.0 x 101
x
3.5 x 10 3
=
7 x 104
0.01
x
0.003
=
.00003
4.2 x 10-3
x
=
x
=
x
2.2 x 10-7
=
9.24 x 10-10
a. Look closely at all the scientific notation rows. Can you determine a simple
way that we can multiply number’s written in scientific notation? If you can,
list the specific rules that you can use to perform these operations.
b. The problems below will allow you to test out your rule. Check your work by
writing each number in standard notations and solving the problem in
standard notation.
Example:
(3.5 x 103)(2.8 x 105) = 9.8 x 108
Standard:
3,500 x 280,000 = 980,000,000
i.
(1.62 x 102)(4.1 x 106) =
Standard:
ii.
(3.45 x 104)(1.75 x 104) =
Standard:
iii.
(1.62 x 10-2)(3.7 x 10-4) =
Standard:
c. Did your method work? If not, can you adjust your rules so that it now
works?
d. Identify similarities between multiplying numbers in scientific notation and
numbers written in exponential form.
2. Complete the following table below. The first row represents multiplication of
numbers written in standard notation. The second row represents multiplication
of numbers written in scientific notation.
Standard
notation
Scientific
notation
Standard
notation
Scientific
notation
400
7.0 x 105
÷
25
=
÷
=
÷
=
÷
2 x 10 3
=
16
3.5 x 102
Standard
notation
Scientific
notation
Standard
notation
Scientific
notation
0.03
4.2 x 10-3
÷
0.003
=
÷
=
÷
=
÷
2.1 x 10-7
=
10
2.0 x 104
a. Look closely at all the scientific notation rows. Can you determine a simple
way that we can divide number’s written in scientific notation? If you can, list
the specific rules that you can use to perform these operations.
b. The problems below will allow you to test out your rule. Check your work by
writing each number in standard notations and solving the problem in
standard notation.
Example:
Standard:
i.
(3.5 x 103) ÷ (2.8 x 105) = 1.25 x 10-2
3,500 ÷ 280,000 = .0125
(1.62 x 102) ÷ (1.35 x 106) =
Standard:
ii.
(3.45 x 108) ÷ (2.875 x 104) =
Standard:
iii.
(8.2 x 10-2) ÷ (2.05 x 10-7) =
Standard:
c. Did your method work? If not, can you adjust your rules so that it now
works?
d. Identify similarities between dividing numbers in scientific notation and
numbers written in exponential form.
3. Sometimes when multiplying and dividing numbers in scientific notation there
needs to be a correction for exponents. The following problems involve correcting
for exponents. Fill in the boxes as before, and see if you can figure out what
correcting the exponent means.
Standard
notation
Scientific
notation
90
Standard
notation
Scientific
notation
5000000
𝑥
200
=
𝑥
𝑥
=
300000
=
=
𝑥
1.8 x 104
1.5 x 1012
a. If you notice, the “corrected” exponent is 1 greater then you would expect.
Why did we need to make this correction?
Standard
notation
Scientific
notation
4,000,000
Standard
notation
Scientific
notation
270000
÷
800
=
÷
÷
÷
=
0.09
5 x 103
=
=
3 x 106
b. If you notice, the “corrected” exponent is 1 less then you would expect. Why
did we need to make this correction?