From standard form to scientific notation:

 

Example: Write the number 300,000,000 in scientific notation. (300,000,000 m/s is the speed of light.)
Solution:
(a) The corresponding number between 1 and 10 is3.0.
(b) For 300,000,000=300,000,000.0 to "become" 3.0 we need to move the decimal point 8 places to the left.
Answer: 300,000,000=3.9 \times 10^8

 

Example: Write the number -23780  in scientific notation.
Solution:
(a) The corresponding number between 1 and 10 is 2.378, or rather -2.378 because we are working with a negative number.
(b) For -23780= -23780.0 to "become" -2.378 we need to move the decimal point 4 places to the left.
Answer: -23780=-2.378 \times 10^4

 

Example: Write the number 0.000000000753  in scientific notation. (0.000000000753 kg is the mass of a dust particle.)
Solution:
(a)The corresponding number between 1 and 10 is 7.53.
(b) For 0.000000000753=0.000\,000\,000\,753 to "become" 7.53 we need to move the decimal point 10 places to the right.
Answer: -0.000000000753=7.53 \times 10^{-10}

 


 

From scientific notation to standard form:

 

Example: Write the number 3.4 \times 10^{-1} in standard form.
Solution:
(a) A negative exponent means we are talking about a "small" number, that is a number between 0 and 1.
(b) We move the decimal point 1 place to the left.
Answer: 3.4 \times 10^{-1}=0.34

 

Example: Write the number1.03 \times 10^6 in standard form.
Solution:
(a) A positive exponent means we are talking about a "big" number.
(b) We move the decimal point 6 places to the right.
Answer: 1.03 \times 10^6 =1,030,000

 

Example: Write the number -2.0 \times 10^{-4} in standard form.
Solution:
(a) A negative exponent means we are talking about a "small" number, that is a number between 0 and 1; the minus sign means we are talking about a negative number. So the result must be a number between -1 and 0.
(b) We move the decimal point 4 places to the left.
Answer: -2.0 \times 10^{-4} = -0.0002


Page last modified on May 18, 2007, at 02:49 AM