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Scientific Notation
 

In chemistry, we often use numbers that are either very large (1 mole = 602 200 000 000 000 000 000 000 particles) or very small (the mass of an electron = 0.000 000 000 000 000 000 000 000 000 000 910 939 kg). Writing numbers with so many digits would be tedious and difficult. To make writing very large and small numbers easier, scientists use an abbreviation method known as scientific notation. In scientific notation the numbers mentioned above would be written as 6.022 x 1023 and 9.10939 x 10-31. As you can see these numbers are written as powers of ten. The power of ten is used because as you move one place to the right or left of a number you are changing by a value of ten. (1 x10 = 10 x10 =100 x10 = 1000 x10 = 10000… or 1 ÷10 = 0.1 ÷10 = 0.01 ÷10 = 0.001 ÷10 = 0.0001…)

Converting a number to or from scientific notation:
· If you move the decimal place to the left, the power of 10 value increases.
· If you move the decimal place to the right, the power of 10 value decreases.

To remember this, think: Left (sounds like lift) something Up and Right (sounds like write) something Down

Example:
Let’s look at the first number from above: 602 200 000 000 000 000 000 000
To put this number in scientific notation you would move your decimal place until there is one number to the left of the decimal. To do this, we must move our decimal 23 places to the left. When you move your decimal to the left, the power of 10 value increases. It increases from 0 to 23. Thus, our answer is 6.022 x 1023

Let’s look at the second number from above: 0.000 000 000 000 000 000 000 000 000 000 910 939
To put this number in scientific notation we must move our decimal 31 places to the right. REMEMBER: You must always have one number to the left of the decimal when writing numbers in scientific notation. Since we are moving our decimal to the right, we must decrease our power of 10 value. It decreases from 0 to –31. Our answer is 9.10939 x 10-31

Rules for multiplying & dividing using scientific notation:

  • When multiplying two numbers in scientific notation, you ADD their powers of 10.
  • For example: (3.45 x 106) x (4.3 x 105) = 14.835 x 1011. But, we must also remember to express our answer in significant figures. Thus, the final answer is 1.5 x 1012
  • When dividing numbers in scientific notation, you SUBTRACT the denominator’s power of 10 value from the numerator’s power of 10 value.
  • For example: (2.898 x 1012) ÷ (3.45 x 1015) = 0.840 x 10-3 (I had to add the zero at the end to get the three significant figures needed.) I got 10-3 because 12 – 15 = –3. Make sure your answer is in proper scientific notation (one number to the left of the decimal). In this problem we have to move the decimal one place to the right. When we move our decimal to the right, we decrease our power of 10. –3 decreases by 1 to –4. Our final answer is: 8.40 x 10-4


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