Science 10 Enriched: SCIENTIFIC NOTATION & SIGNIFICANT FIGURES
Scientific Notation Review
Scientific notation is the way that scientists easily handle very large numbers or very small numbers. For example,
instead of writing 0.0000000056, we write 5.6 x 10-9. So, how does this work?
We can think of 5.6 x 10-9 as the product of two numbers: 5.6 (the digit term) and 10-9 (the exponential term).
Here are some examples of scientific notation.
10000 = 1 x 104
24327 = 2.4327 x 104
1000 = 1 x 103
7354 = 7.354 x 103
100 = 1 x 102
482 = 4.82 x 102
10 = 1 x 101
89 = 8.9 x 101 (not usually done)
1 = 100
1/10 = 0.1 = 1 x 10-1
0.32 = 3.2 x 10-1 (not usually done)
1/100 = 0.01 = 1 x 10-2
0.053 = 5.3 x 10-2
1/1000 = 0.001 = 1 x 10-3
0.0078 = 7.8 x 10-3
1/10000 = 0.0001 = 1 x 10-4
0.00044 = 4.4 x 10-4
As you can see, the exponent of 10 is the number of places the decimal point must be shifted to give the
number in long form. A positive exponent shows that the decimal point is shifted that number of places to the
right. A negative exponent shows that the decimal point is shifted that number of places to the left.
In scientific notation, the digit term indicates the number of significant figures in the number. The exponential
term only places the decimal point. As an example,
46600000 = 4.66 x 107
This number only has 3 significant figures. The zeros are not significant; they are only holding a place. As
another example,
0.00053 = 5.3 x 10-4
This number has 2 significant figures. The zeros are only place holders
Convert the following numbers into scientific notation:
1) 3,400
_______________________________
2) 0.000023
_______________________________
3) 101,000
_______________________________
4) 0.010
_______________________________
5) 45.01
_______________________________
6) 1,000,000
_______________________________
7) 0.00671
_______________________________
8) 4.50
_______________________________
Convert the following numbers into standard notation:
9) 2.30 x 104
_______________________________
10) 1.76 x 10-3
_______________________________
11) 1.901 x 10-7
_______________________________
12) 8.65 x 10-1
_______________________________
13) 9.11 x 103
_______________________________
14) 5.40 x 103
_______________________________
15) 1.76 x 104
_______________________________
16) 7.4 x 10-5
_______________________________
Significant Figures
Summary: associated with every measurement made is some degree of uncertainty. For instance, you might measure the length of
the dark line shown in the diagram as 20.7 cm. The digits 2 and 0 are certain - there is no doubt that the length is "20 point
something" cm. The 7 is uncertain - it might be a little less or a little more. The number of ‘significant digits’ indicates the certainty of
our measurement. There are three significant digits in this case (20.7). Thus, significant digits in a measurement or calculation
consist of all those digits that are certain, plus one uncertain digit. Although your calculator may give you an answer to eight decimal
places or more, you should not include all of these digits in your answer.
Rules For Determining The Number Of Significant Figures
1. All digits from 1 to 9 (non-zero digits) are considered to be significant.
EX. 1.23g = 3 sig figs
2. Zeros between non-zero digits are always significant
EX. 1.03 g = 3 sig figs
3. Zeros to the left of non zero digits, serve only to locate the decimal point; they are not significant.
EX. 0.00123g = 3 sig figs
4. Any zero printed to the right of a non-zero digit is significant if it is also to the right of the decimal point.
EX. 2.0 g and 0.020 g each have 2 sig figs.
5. Any zero printed to the right of a non-zero digit are not significant unless indicated specifically by writing the
number in scientific notation.
EX. 100 g = 1 sig fig. BUT: 1 x 102 g = 1 sig fig, 1.0 x 102 g = 2 sig figs, 1.00 x 102 g = 3 sig figs
6. Any number that is counted instead of measured has an infinite number of significant digits.
EX. “3 test tubes” or “2 people” = infinite sig figs! (These values are infinitely precise).
SCIENTIFIC NOTATION RULE: All digits from 1-9, and zeroes that are not placeholders are counted as being
significant. In scientific notation, all numerals written before the “x 10?” are considered significant.
Determine the number of significant figures in the following:
1) 23.7 x 10-2 _________
2) 1.4 x 107
_________
3) 4.293 x 104 _________
4) 705
_________
5) 600
_________
6) 4301.0
_________
7) 0.00056
_________
8) 40280
_________
9) 33214
_________
10) 2.003
_________
MULTIPLYING AND DIVIDING RULE: When multiplying or dividing, your answer may only show as many significant
digits as the multiplied or divided measurement showing the least number of significant digits.
Perform the following calculations and round according to the rule above.
1) 50.0 x 2.00 =
2) 2.3 x 3.45 x 7.42 =
3) 1.0007 x 0.009 =
4) 51 / 7 =
5) 208 / 9.0 =
6) 0.003 / 5 =
ADDING AND SUBTRACTING RULE: When adding or subtracting, your answer must show as many decimal places
as the measurement having the fewest number of decimal places.
Perform the following calculations and round according to the rule above.
1) 2.25 + 6 =
2) .04 + 2.7 =
3) 18.640 + 670.445 =
4) 0.70 - 0.1 =
5) 640 - 627.03 =
6) 12.09 - 6.7 =
Extra Practice
Find the significant figures in the following questions:
1.
a) 0.002020
e) 200
i) 0.1010
b) 3.02000
f) 201
j) 10000
c) 0.001202 x 103
g) 200 x 10-12
k) 304001000
d) 3001
h) 1010
l) 2.00100
2. Perform the following calculations and answer to the correct number of significant figures or decimal
places.
a) ( 100 )(203)/ (1.0034)(35002)
c) (10.0200)(100.0)(0.000023)
e) (98.76 – 100.00)/(100.00)
g) (445 + 34.5)/(45 – 23.45)
b) 1.0002 + .00345
d) 34.98 – 2.34
f) 1.02 + 1.0 + 12 + 196