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!
what is the formula used for this question? "Jamal wants to save $54,000 for a down payment on a home. How much will he need to invest in an account with 8.2% APR, compounding daily, in order to reach his goal in 5 years?"