1. Chapter 3 Scientific Measurement 3.1 Using and Expressing Measurements
3.2 Units of Measurement
3.3 Solving Conversion Problems
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2. Express numbers in scientific and decimal notation.
Learning Target:
Express numbers in scientific and decimal notation.
Designed by Skip Tyler, Varina High School

3. How do you measure a photo finish?
CHEMISTRY & YOU
How do you measure a photo finish?
Sprint times are often measured to the nearest hundredth of a second (0.01 s). Chemistry also requires making accurate and often very small measurements.
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4. SCIENTIFIC NOTATION A QUICK WAY TO WRITE REALLY, REALLY BIG OR
REALLY, REALLY SMALL NUMBERS.

5. How wide is our universe?
210,000,000,000,000,000,000,000 miles (22 zeros) This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.

6. Mathematicians are Lazy!!!
They decided that by using powers of 10, they can create short versions of long numbers.

7. Scientific Notation Scientific Notation
How do you write numbers in scientific notation?
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8. Scientific Notation A measurement -
Your height (66 inches), your age (15 years), and your body temperature (37°C) are examples of measurements.
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9. Scientific Notation
In chemistry, you will often encounter very large or very small numbers.
A single gram of hydrogen, for example, contains approximately 602,000,000,000,000,000,000,000 hydrogen atoms.
You can work more easily with very large or very small numbers by writing them in scientific notation.
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10. Scientific Notation
A number is expressed in scientific notation when it is in the form
a x 10n
a = ….
n = …..

11. Rules for Scientific Notation
To be in proper scientific notation the number must be written with
1. ….
2. ….
3. ….
23 X 105 is not in proper scientific notation. Why?

12. Write the width of the universe in scientific notation.
210,000,000,000,000,000,000,000 miles Where is the decimal point now? ….. Where would you put the decimal to make this number be between 1 and 10?

13. Scientific Notation In scientific notation, -
For example, the number 602,000,000,000,000,000,000,000 can be written in scientific notation as 6.02 x 1023.
The coefficient =
The power =
The Exponent =

14. Scientific Notation
In scientific notation, the coefficient is always a number greater than or equal to one and less than ten. The exponent is an integer.
A positive exponent indicates how many times the coefficient must be … by 10.
Move Decimal to the ….
A negative exponent indicates how many times the coefficient must be …. by 10.
Move Decimal to the …..
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15. 210,000,000,000,000,000,000,000
How many decimal places did you move the decimal? When the original number is more than 1, the exponent is positive. The answer in scientific notation is

16. 1) Express 0.0000000902 in scientific notation.
Where would the decimal go to make the number be between 1 and 10? The decimal was moved how many places? When the original number is less than 1, the exponent is negative.

17. Write 28750.9 in scientific notation.
x 10-5
x 10-4
x 104
x 105

18. Write 531.42 x 105 in scientific notation.

19. Soooo
137,000,000 can be rewritten as

20. Using scientific notation, rewrite the following numbers.
Now You Try
Using scientific notation, rewrite the following numbers.
A. 347,000.
B. 902,000,000.
C. 61,400.

21. Convert these:
A X 105 B X 106

22. Try These
A. 4,000
B X 103
C X 106
D. 306,000,000

23. In the United States, 15,000,000 households use private wells for their water supply. Write this number in scientific notation.

24. The U.S. has a total of X 107 acres of land reserved for state parks. Write this in standard form.

25. Why does a Negative Exponent give us a small number?
10000 = 10 x 10 x 10 x 10 = 104
= 10 x 10 x 10 = 103
= 10 x 10 = 102
= 101
1 = 100
Do you see a pattern?

26. Using Scientific Notation, rewrite the following numbers.
Your Turn
Using Scientific Notation,
rewrite the following numbers. A B C

27. More Examples B) 1.248 X 10-6 C) 6.123 X 10-5 D) 0.00000306

28. The nucleus of a human cell is about 7 X 10-6 meters in diameter
The nucleus of a human cell is about 7 X 10-6 meters in diameter. What is the length in standard notation?
…….

29. A ribosome, another part of a cell, is about 0
A ribosome, another part of a cell, is about of a meter in diameter. Write the length in scientific notation. …..

30. Scientific Notation
When writing numbers greater than ten in scientific notation, the exponent is positive and equals the number of places that the original decimal point has been moved to the left. 6,300,000. = 6.3 x ,700. = 9.47 x 104
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31. Scientific Notation
Numbers less than one have a negative exponent when written in scientific notation. The value of the exponent equals the number of places the decimal has been moved to the right = 8 x 10– = 7.36 x 10–3
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