Be careful not to include the leading 0 in your count. We move the decimal point 13 places to the right, so the exponent of 10 is 13. The exponent is negative because we moved the decimal point to the right. This is what we should expect for a small number.
A number is written in
scientific notation if it is written in the form
$\text{\hspace{0.17em}}a\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}{10}^{n},$ where
$\text{\hspace{0.17em}}1\le \left|a\right|<10\text{\hspace{0.17em}}$ and
$\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$ is an integer.
Converting standard notation to scientific notation
Write each number in scientific notation.
Distance to Andromeda Galaxy from Earth: 24,000,000,000,000,000,000,000 m
Diameter of Andromeda Galaxy: 1,300,000,000,000,000,000,000 m
Number of stars in Andromeda Galaxy: 1,000,000,000,000
Diameter of electron: 0.00000000000094 m
Probability of being struck by lightning in any single year: 0.00000143
To convert a number in
scientific notation to standard notation, simply reverse the process. Move the decimal
$\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$ places to the right if
$\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$ is positive or
$\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$ places to the left if
$\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$ is negative and add zeros as needed. Remember, if
$\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$ is positive, the value of the number is greater than 1, and if
$\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$ is negative, the value of the number is less than one.
Converting scientific notation to standard notation
Convert each number in scientific notation to standard notation.
Scientific notation, used with the rules of exponents, makes calculating with large or small numbers much easier than doing so using standard notation. For example, suppose we are asked to calculate the number of atoms in 1 L of water. Each water molecule contains 3 atoms (2 hydrogen and 1 oxygen). The average drop of water contains around
$\text{\hspace{0.17em}}1.32\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}{10}^{21}\text{\hspace{0.17em}}$ molecules of water and 1 L of water holds about
$\text{\hspace{0.17em}}1.22\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}{10}^{4}\text{\hspace{0.17em}}$ average drops. Therefore, there are approximately
$\text{\hspace{0.17em}}3\cdot \left(1.32\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}{10}^{21}\right)\cdot \left(1.22\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}{10}^{4}\right)\approx 4.83\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}{10}^{25}\text{\hspace{0.17em}}$ atoms in 1 L of water. We simply multiply the decimal terms and add the exponents. Imagine having to perform the calculation without using scientific notation!
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
I'm 13 and I understand it great
AJ
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
Atone
hi
Adu
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
Vedant
find the 15th term of the geometric sequince whose first is 18 and last term of 387