Scientific Notation Notes

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There is a mathematical scientific notation which is very useful for writing very big and very small numbers.

Scientific notation is an abriviation. Short way to put numbers that are really big and really small.

Example:

25, 300, 000, 000, 000 miles

25, 300, 000, 000, 000. Place the decimal point and move it to the left.

2.5, 300, 000, 000, 000 Move it until there is only one digit on the left side of the decimal point.

2.5 300 000 000 000 Count how many numbers you move the decimal point.

25, 300, 000, 000, 000 = 2.53 and get rid of the ceros. 2.53 X 10+13

0.000 000 0203 seconds

0.000 000 0203 Move the decimal point to the right until there is any cero at the right of the decimal point.

2.03 X 10-8

move move

exponent goes UP + <------- . -------> - exponent goes down

left right

3 749 000 000 = 3.749 X 10+9

0.00005269 = 5.269 X 10-5

813 000 000 000 000 = 8.13 X 10+14

0.000 000 0214 = 2.14 X 10-8

0.004 = 4.0 X 10-3

0.000000000000000123 = 1.23 X10-16

452000000000000 = 4.52 X 10+14

698.254000000000000000 = 6.98254 X 10+2

3.28 X 10+8 = 328000000

8.45 X 10-3 = 0.00845

8.45 X 10+5 = 845 000

1.2 X 10-8 = 0.00000012

1.54 X 10+8 = 154 000 000

-5.13 X 10+6 = -5130 000

-0.00942 = -9.42 X 10-3

- 0.0949 = -9.49 X 10-2

698000 = 6.98 X 10+5

-0.0763 = -7.63 X 10-2

9110 = 9.11 X 10+3

-4.66 X 10+4 = -46600

9.01 X 10+3 = 9010

-9.9 X 10 -3 = 0.0093

-0.598 = - 5.98 X 10-1

3.31 X 10-1 = 0.331

- 8.31 = -8.31 X 10+0

-0.00818 = -8.18 X 10-3

1.73 0+3 = 1730

-137000 = -1.37 X 10+5