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.
Scientific notation
A number is written in
scientific notation if it is written in the form
where
and
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
places to the right if
is positive or
places to the left if
is negative and add zeros as needed. Remember, if
is positive, the value of the number is greater than 1, and if
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
molecules of water and 1 L of water holds about
average drops. Therefore, there are approximately
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!
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ...
Step 2: Find each score's deviation from the mean. ...
Step 3: Square each deviation from the mean. ...
Step 4: Find the sum of squares. ...
Step 5: Divide the sum of squares by n – 1 or N.
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400
a. what is the probability of getting more than 12,000 hits?
b. what is the probability of getting fewer than 9,000 hits?
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits