Scientific Notation

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Scientific notation is a way of expressing very large or very small numbers which are awkward to say and write.

For example, the mass of an electron is 0.0000000000000000000000000000009109 kg. This is a very small number.  Trying to say this number using place values is difficult

Another example is 55,000,000,000. It is the number of hamburgers sold by McDonald's.

When we write a number in scientific notation, we express it in the following form:            

where N is some number greater than or equal to 1 but less than 10 (1< N < 10)and b is some integer (a positive or negative whole number exponent).

Steps for Writing a number in scientific notation

1. Starting with the number in decimal format, move the decimal point until the number is between 1 and 10, including 1.

2. Multiply the number formed in step 1 by 10 raised to the number of decimal places moved. If the original number was between 0 and 1, the power of 10 is negative. If the original number was greater than 1, the power is positive

3. This procedure is for a positive number. If the original number is negative, perform steps 1 and 2 as if the number is positive, then append a negative sign to the result.

ExamplesWrite each of the following numbers in scientific notation:(a) 93,000,000 (b) .00005144 (c) -33,452.8Solutions

                                                                                             

       

To change a number from scientific notation back into decimal form, we reverse the steps.

ExamplesWrite the following in decimal form:                                              Solutions

                                                                    

       

Steps for Multiplying and Dividing numbers in scientific Notation

1. Write each number in scientific notation if not already expressed as such

2. On a calculator, multiply or divide the decimal parts

3. If multiplying, apply the product rule for exponents on the powers of 10

4. If dividing, apply the quotient rule for exponents on the powers of 10.

5. Express the answer in scientific notation.

Examples

                                                                                                       

Solutions