Scientific Notation Examples

1) **264 000**

M x 10^{n}

2.64 x 10^{5}

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 10^{n}

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 10^{n}

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 10^{3}

6.2000 x 10^{4}

__+ 5.2 x 10 ^{1}__

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

2.610 x 10

62.000 x 10

+

Multiplication Using Scientific Notation

(3.2 x 10

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 10^{5}

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 10^{3}) + (3.4 x 10^{4})

f) (2.9 x 10^{-4}) - (6.4 x 10^{-5})

g) ((2.6) x (2.6 x 10^{2})) / 0.000 026

h) (2.73 x 10^{4)} / (9.10 x 10^{-2})

i) (3.2 x 10^{-3}) x (1.5 x 10^{-2})