Writing And Evaluating Scientific Notation Worksheet Page 2
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15Multiplying and Dividing Powers of 10
Multiplying powers of 10 simply requires adding exponents.
For example:
x
= 10,000 x 10,000,000 = 100,000,000,000
7
10
4
10
4
7
=
10
10
10
4 + 7
10
11
x 10
= 100,000 x 0.001 =
100
10
5
-‐ 3
5
-‐ 3
5 + ( -‐ 3)
= 10
= 10
2
10
10
x
= 0.00000001 x 0.00001 = 0.0000000000001
10
-‐ 8
10
-‐ 5
-8
-5
-13
10
10
10
Dividing powers of 10 requires subtracting exponents.
For example:
5
10
= 100,00
1,000 =
100
10
3
÷
10
5
10
3
= 10
5 -‐ 3
= 10
2
10
3
= 1,000
10,000,000 = 0.0001
7
÷
10
3
7
= 10
3 -‐ 7
= 10
-‐ 4
10
10
10
-‐ 4
= 0.0001
0.000001 =
100
-‐ 6
÷
10
-4
-6
=
-4 - (-6) =
2
10
10
10
10
Powers of Powers of 10
We can use the multiplication and division rules to raise powers of 10
to other powers. For example:
3
4
= 10
x 10
x 10
=
=
(10
)
4
4
4
4 + 4 + 4
10
12
10
Note that we get the same result by simply multiplying the two
powers:
3
4
=
=
(10
)
4x3
10
12
10
Adding and Subtracting Powers of 10
There is no shortcut for adding or subtracting powers of 10, as there
is for multiplication or division. The values must be written in
longhand notation. For example:
+
= 1,000,000 + 100 = 1,000,100
10
6
10
2
+ 10
= 100,000,000 + 0.001 = 100,000,000.001
10
8
-‐ 3
-
= 10,000,000 – 1,000 = 9,999,000
7
10
10
3
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