Scientific Notation Examples

1) 264 000

M x 10n

2.64 x 105

M must be between 1 and 10; the exponent of 10 indicates the number of places you moved the decimal point to convert 264 000 to 2.64 x 10; the exponent is positive because you moved the decimal point to the left.

2) 0.0716

M x 10n

7.16 x 10 -2

M must be between 1 and 10; the exponent of 10 indicates the number of places you moved the decimal point to convert 0.0716 to 7.16 x 10; the exponent is negative because you moved the decimal point to the right.

3) 0.000 000 132

M x 10n

1.32 x 10-7

M must be between 1 and 10; the exponent of 10 indicates the number of places you moved the decimal point to convert 0.000 000 132 to 1.32 x 10; the exponent is negative because you moved the decimal point to the right.

Adding/Subtracting Using Scientific Notation

2.610 x 103
6.2000 x 104
+ 5.2 x 101

all numbers must have the same exponent of 10 before you can add or subtract and so the above becomes

2.610 x 103
62.000 x 103
+ 0.052 x 103
64.662 x 103 which must be changed to 6.4662 x 104

Multiplication Using Scientific Notation

(3.2 x 103) (1.5 x 102)

Multiply the M values and then agebraically combine the exponents of ten while keeping the x 10.

Multiple 3.2 by 1.5 to get 4.8
Algebraically add the exponents of 10 to get 3 +2 = 5

Ans: 4.8 x 105

Dividing Using Scientific Notation

(8.4 x 10-7) / (2.1 x 10-4)
Divide the M values and then subtract the exponent of the denominator from the exponent of the numerator.

Divide 8.4 by 2.1 and get 4.0
Subtract the exponents (-7 -(-4)) gives us -3

Ans: 4.0 x 10-3

Practice Problems:

Convert the following into scientific notation:
a) 1 930
b) 262 000
c) 71 400
d) 93 100 000
e) 704
f) 0.0713
g) 0.000 067 2
h) 0.195
i) 0.000 000 008 33
j) 0.006 21

Evaluate the following and express the results in scientific notation:

a) 8 200 x 510
b) 910 x 0.000 30
c) 720 / 36 000
d) 3 100 / 0.012
e) (2.6 x 103) + (3.4 x 104)
f) (2.9 x 10-4) - (6.4 x 10-5)
g) ((2.6) x (2.6 x 102)) / 0.000 026
h) (2.73 x 104) / (9.10 x 10-2)
i) (3.2 x 10-3) x (1.5 x 10-2)