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Mastering Scientific Notation: Conversions and Calculations

Learn how to convert numbers to scientific notation easily, understand the power of tens, and practice with sample problems. Perfect for mastering calculations in chemistry and scientific math!

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Mastering Scientific Notation: Conversions and Calculations

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  1. Calculations in Chemistry Scientific Math

  2. I CAN convert number to and from SCIENTIFIC NOTATION.

  3. What are Measurements • A measurement is a QUANTITY with both a NUMBER and a UNIT. • In science, you will encounter very, very large numbers as well as very, very small ones. • To simply the handling of such numbers, we often write them in a compressed form called SCIENTIFIC NOTATION.

  4. In scientific notation, numbers with many digits are often written as a coefficient and a power of 10. • Example 6.022 x 1023 • Coefficient • Power of 10

  5. Converting Numbers to Scientific Notation • Converting numbers to scientific notation is easy. • 1. Locate the DECIMAL [may be an understood decimal] • 2. MOVE the decimal to the LEFT or to the RIGHT until it is to the RIGHT OF THE FIRSTNON-ZERO DIGIT in the number. • Example 24567.88 would be 2.456788 • 3. COUNT THE NUMBER OF PLACES the decimal was moved…this is the POWER OF 10.

  6. When the decimal is moved to the LEFT the power of 10 is POSITIVE. • When the decimal is moved to the RIGHT the power of 10 is NEGATIVE. • You may DROP TERMINAL ZEROS to round off or follow the directions in the problem.

  7. SAMPLE PROBLEM • Convert this number to scientific notation: • 602200000000000000000000 • Locate the decimal. • Decide if the decimal needs to move left or right. • Count the number of places it has to move. • Rewrite the number with the decimal in its new location [drop terminal zeros]. • Add the power of 10 with the correct sign.

  8. 602200000000000000000000 • Since there was no written decimal it is understood to be at the end of the number. • Which direction should it be moved? • We will need to move it toward the LEFT to get it between the first two non-zero digits. • 602200000000000000000000 • The decimal was moved a total of 23 places to the left.

  9. 6 02200000000000000000000 • Drop the terminal zeros to get • 6 022 • Since the decimal moved 23 places to the LEFT, the power of 10 is POSITIVE 23.

  10. So the number in scientific notation is: 6.022 X 1023

  11. MORE PRACTICE • Write this number is Scientific Notation: • 0.0000475000

  12. 0.0000475000 • Decimal First two non-zero digits • This time the decimal has to be moved to the RIGHT. This will make the power of 10 NEGATIVE. • 000004.75000 • DROP these zeros!

  13. 4.75 • The decimal was moved 5 places to the right, so the power of 10 is -5. • 4.75 X 10-5

  14. Write each number in scientific notation. 0.07882 = 0.00000272338 = 118000 = 87200 = 0.00002786 = 0.000000664 = 450 = 74171.7 = 770 = 0.0000085 =

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