1. Base unit [gram (g), meter(m), liter (l), etc.] x100
Question Of the Day:
Write the following numbers in scientific notation:
143.0
Convert the following:
1 μm = m
0.001 A = mA
1hm = m
Prefix
Symbol
Scientific Notation
giga G
109
mega M
106
Kilo k
103
hecto h
102
deca da
101
Base unit [gram (g), meter(m), liter (l), etc.] x100
deci d
10-1
centi c
10-2
milli m
10-3
micro μ
10-6
nano n
10-9
pico p
10-12

2. Base unit [gram (g), meter(m), liter (l), etc.] x100
Answers
Write the following numbers in scientific notation:
=> 4.12 x 10 -4
143.0 => 1.43 x 10 2
=> 1.2 x 1010
Convert the following:
1 μm = m
0.001 A = 1mA
1hm = 100 m
Prefix
Symbol
Scientific Notation
giga G
109
mega M
106
Kilo k
103
hecto h
102
deca da
101
Base unit [gram (g), meter(m), liter (l), etc.] x100
deci d
10-1
centi c
10-2
milli m
10-3
micro μ
10-6
nano n
10-9
pico p
10-12

3. Significant Figures and
Real Life

4. RULES Rule 1: All nonzero numbers are significant.
Examples: 4328, 38273, 1234
Rule 2: All zeros that are “sandwiched” or between two nonzero numbers are significant.
Examples: 303, 23903, 9401
Rule 3: Trailing zeros are significant if the number contains a decimal.
Examples: , , 10. , 3000.
Not examples: 10, 3000, 870

5. Rule 4: Leading zeros that function only to hold the decimal point are NOT significant.
Example: 0.009, 0.65
Rule 5: Zeros that are in a decimal number that are after a nonzero digit are significant.
Examples: 0.906,
Rule 6: If a number is written in scientific notation then all numbers to the left of the multiplication sign are significant.
Examples: 1.03 x 102

6. Let’s Talk About Rounding
What if I have the number and I want it written with only 3 significant figures.
Which digit would I have to round?
What are the rules of rounding?
Rule 1: If the digit you are rounding is followed by a 0, 1, 2, 3, or 4 then the digit you are rounding stays the same. All the digits after the rounded digit becoms zero.
For example, if you are rounding 452 to the nearest tens then the number becomes 450.
Rule 2: If the digit you are rounding is followed by a 5, 6, 7, 8, or 9 then the digit you are rounding increases by one. All digits after the rounded digit become zero.
For example, if you are rounding 452 to the nearest hundreds then the number becomes 500.

7. So… Back to the Original Question
What if I have the number and I want it written with only 3 significant figures.
Which digit would I have to round?
If I wanted three sig. figs the number would be written as
How could we put into scientific notation using only 3 sig. figs.
2.45 x 10 8

8. Another example:
Write into scientific notation with only 4 sig figs.
This becomes

9. Now Try These:
Write each number 3 sig figs, then put the number into scientific notation!

10. WHY?
Scientists do a lot of measuring. When scientists use an instrument (such as a ruler, graduated cylinder, spectrophotometer or balance) to measure something, it is important to take full advantage of the instrument. However, they can’t cheat and record a better measurement than the instrument is capable of. There is an understanding among scientists of the proper way to record valid measurements from any instrument. When you are the scientist, you must record data in this way. When you are reading other scientists’ work, you must assume they recorded their data in this way.

11. Ruler A
Example: In a lab we have to measure the length of this Mg strip. Using the ruler, how long do you think this piece of Mg is?

12. Are we certain of these values?
From the values listed on the board do you think that there was any agreement between any of these values?

13. Rule of Thumb
When a measurement is recorded properly, all of the digits that are read directly (certain) and one
estimated (uncertain) digit are called significant digits. The number of allowable significant digits is
determined by the marks or gradations of the instrument. Sometimes a “0” is the estimated digit and
must be recorded.

14. Ruler B Make an estimation of the length of the Mg strip.
What number(s) are we certain of here?
What number(s) is uncertain?

15. THINK ABOUT IT
When humans use measuring instruments, variation is expected. Everyone will estimate differently between marks on the instrument. On the other hand, digits that are certain (based on marks on the instrument) should not vary from person to person.

16. Ruler C Make an estimation of the length of the Mg strip.
What number(s) are we certain of here?
What number(s) is uncertain?

18. PRACTICE