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!
Questions & Answers
How look for the general solution of a trig function
hi can you give another equation I'd like to solve it
Daniel
what is the value of x in 4x-2+3
Olaiya
if 4x-2+3 = 0
then
4x = 2-3
4x = -1
x = -(1÷4) is the answer.
Jacob
4x-2+3
4x=-3+2
4×=-1
4×/4=-1/4
LUTHO
then x=-1/4
LUTHO
4x-2+3
4x=-3+2
4x=-1
4x÷4=-1÷4
x=-1÷4
LUTHO
A research student is working with a culture of bacteria that doubles in size every twenty minutes. The initial population count was 1350 bacteria. Rounding to five significant digits, write an exponential equation representing this situation. To the nearest whole number, what is the population size after 3 hours?
A guy wire for a suspension bridge runs from the ground diagonally to the top of the closest pylon to make a triangle. We can use the Pythagorean Theorem to find the length of guy wire needed. The square of the distance between the wire on the ground and the pylon on the ground is 90,000 feet. The square of the height of the pylon is 160,000 feet. So, the length of the guy wire can be found by evaluating √(90000+160000). What is the length of the guy wire?