SCIENTIFIC NOTATION NOTES

 

BIG and small numbers

§       Do you know this number: 300,000,000 meters per second?

§       It's the Speed of light !

§       Do you recognize this number, 0.000000000 753 kg. ?

§       This is the mass of a dust particle underneath your bed!

§       Scientists and mathematicians have developed a shorter method to express very large and very small numbers. This method is called scientific notation.

§       Scientific Notation is based on powers of 10.

Scientific notation consists of two parts:

^§         A number between 1 and 10 AND A power of 10 N x 10^x

To write BIG numbers in scientific notation:

§       123,000,000,000

§       Put the decimal after the first digit

§       To find the exponent, count the number of places from the decimal to the end of the number. Use the ‘loop de loo’ method.

§       In 123,000,000,000 there are 11 places after the 1.

^§         Therefore we write 123,000,000,000 as:     1.23 x 10 ¹¹

^§         You can drop the zeros after the ‘3’, however, if there were other digits other than 0 you would have to include them such as 123000400000 would be 1.230004 x 10¹¹

To convert very small numbers (bacteria, virus, electrons)

§       0.000567

§       Put the decimal after the first digit and drop the zeroes (this time the zeroes are in front)   5.67

§       Count the number of places from the decimal to the beginning of the number (moved 4 places)

§       Answer: 5.67 x 10^-4

§       The exponent is negative because you are multiplying by a fraction