Scientific Notation
Published on Nov 19, 2015
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Converting standard form to scientific notation
- to convert standard to scientific notation, you have to take your number and move the decimal until there is only one number left in front of it. Then with that number you put a multiplication sign next to it then next to the multiplication sign you put a 10, after that you count how many times it took you to move the decimal point and once you find that out that's your exponent above the 10
*Example- 1) 3,102,000,000 - 3.102
3.102 x 10 with an exponent of 9
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Converting from scientific notation to standard
- to convert from scientific notation to standard form you have to look at your 10 and the exponent and if the exponent is positive you move the decimal of your number to the right and if the exponent is negative you move the decimal of your number to the left. Once you follow those procedures and you have moved the decimal to where it needs to be that is your final answer in standard form
*Examples- 1) 4.603 x 10 to the exponent of 11
4.60300000000 - 460,300,000,000
2) 4.603 x 10 to the exponent of -11
4.603 - .00000000004603
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Adding and subtracting expressions in scientific notation
- for adding in scientific notation you first look at your exponents to see if they are the same or not, if they are the same you look at your other two numbers and add them together once you get that answer you bring down the 10 and the exponent and in between the number you got, the 10 and the exponent you will put a multiplication sign and that will be your your final answer
*Example- 1) (3.7696 x 10 to the 5th)+(4.212 x 10 5th)
3.7696 + 4.212 = 7.9816
7.9816 x 10 with an exponent of 5
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Adding and subtracting expressions in scientific notation
- for subtracting in scientific notation you first look at your exponents to see if they are the same or different, if the exponents are the same you look at your other two numbers and subtract them and once you get your answer you bring down the 10 and the exponent. Then in between the number you got, the 10 and the exponent you put a multiplication sign and that's your answer
*Example- 1) (1.55 x 10 to the 7th) - (7.2 x 10 to 7th)
1.55 - 7.2 = 5.65
5.65 x 10 with an exponent of 7
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Multiplying and dividing expressions in scientific notation
- for multiplying in scientific notation you first look at your exponents to see if they are the same or different, if they are different you just add the exponents together then from that number you get that's the new exponent above the 10. Now for the other two numbers you multiply them together and the answer you get from that you bring it down and put a multiplying sign next to it bring down the 10 and the exponent and that is your final answer
*Example- 1) (4 x 10 to the 4th)(6 x 10 to the 2nd)
4 x 6 x 10 to 4th x 10 to 2nd
24 x 10 with an exponent of 6
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Multiplying and dividing expressions in scientific notation
- for dividing in scientific notation you have to subtract the exponents and divide the coefficients after that you have you final answer
*Examples- 1) 9 x 10 to the 14th
3 x 10 to the 7th
3 x 10 with an exponent of 7
2) 5 x 10 to the 6th
4 x 10 to the 3rd
1.25 x 10 with an exponent of 3
Photo by Bryan Davidson
5 real world examples
- 1) astronomers use scientific notation
- 2) sociologists use it
- 3) engineers use scientific notation
Photo by Amir Kuckovic
