Tuesday, October 30, 2012
When numbers get very large or very small, they become difficult to work with and read. Examples of such
numbers are 0.0000000000043425 and 546,245,000,000,000,000,000. Oftentimes these types of numbers appear in science, such as the distance planets are from Earth or the mass of atoms. Scientific notation is a method to make using such numbers easier by writing them in a simpler form. A positive number in the form N times 10^x , where 1 ≤ N < 10 and x is an integer, is said to be in scientific notation.
When a number is in scientific notation, the decimal point is always after the first non zero number. Some
examples of numbers in scientific notation are
3.5 X 10^3, 5.89 X 10^(-4) and 2.9123 X 10^6
To change a number into scientific notation, we move the decimal point between the first two non zero
numbers. Then we count the number and direction that the decimal point must move to get the original number.
The number of decimal places moved will be the exponent. If we move the decimal point to the right, the
exponent is positive. If we move the decimal point to the left, the exponent is negative.
Examples: Write the following numbers in scientific notation.
First place the decimal point between the 5 and 6. Count how many decimal places we have to move to
the right to get to the end of the number. Notice we have to move 17 decimal places. Therefore,
567,325,000,000,000,000 written in scientific notation is 5.67325 X 10^17.
•Note that the zeros after the 5 are not written when changing to scientific notation. When all the rest of
the numbers are zero they are not written.
First place the decimal point between the 7 and 9. Count how many decimal places we have to move to
the left to get back to the beginning of the number. Notice we have to move 10 decimal places.
Therefore 0.0000000007982 written in scientific notation is 7.982 X 10^(-10) .
Be sure to be careful with numbers such as 65.8 X 10^3 and 254.69 X 10^(-4). At first glance, these appear to be in scientific notation, but the decimal point is not after the first non zero number.
To write in scientific notation, multiply the problem out and then convert to scientific notation.
65.8 X 10^3 = 65.8 X 1000 = 65,800
Another way to simplify the above is to move the decimal point 3 places to the right since the exponent is 3.
Now we can change 65,800 into scientific notation, which is 6.58 X 10^4.
In the example 254.69 X 10^(-4), multiply to get 254.69 X 0.0001 = 0.025469.
Another way to simplify the above is to move the decimal point 4 places to the left since the exponent is -4.
Now we can change 0.025469 into scientific notation, which is 2.5469 X 10^(-2) .
In some cases, using scientific notation makes multiplying and dividing very large or very small numbers easier.