Question

chemquest 2
significant figures
name: ave brean date: 9 - 09 - 05 hour: 2
information: significant figures
we saw in the last chemquest that scientific notation can be a very nice way of getting rid of unnecessary zeros in a number. for example, consider how convenient it is to write the following numbers:
32,450,000,000,000,000,000,000,000,000 = 3.245 x 10^24
0.000000000000000127 = 1.27 x 10^-16
there are a whole lot of zeros in the above numbers that are not really needed. as another example, consider the affect of changing units:
21,500 meters = 21.5 kilometers
0.00582 meters = 5.82 millimeters
notice that the zeros in \21,500 meters\ and in \0.00582 meters\ are not really needed when the units change. taking these examples into account, we can introduce three general rules:

1. zeros at the beginning of a number are never significant (important).
2. zeros at the end of a number are not significant unless... (youll find out later)
3. zeros that are between two nonzero numbers are always significant.

therefore, the number 21,500 has three significant figures: only three of the digits are important—the two, the one, and the five. the number 10,210 has four significant figures because only the zero at the end is considered not significant. all of the digits in the number 10,005 are significant because the zeros are in between two nonzero numbers (rule #3).
critical thinking questions

1. verify that each of the following numbers contains four significant figures. circle the digits that are significant.

a) 0.00004182 b) 494,100,000 c) 32,010,000,000 d) 0.00003002

1. how many significant figures are in each of the following numbers?

a) 0.000015045 b) 4,600,000 c) 2406
d) 0.000005 e) 0.0300001 f) 12,000
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Explanation:

Step1: Analyze number a (0.00004182)

Leading zeros are not significant. So 4, 1, 8, 2 are significant.

Step2: Analyze number b (494,100,000)

Trailing zeros without a decimal point may not be significant. 4, 9, 4, 1 are significant.

Step3: Analyze number c (32,010,000,000)

Zeros between non - zero digits are significant. 3, 2, 0, 1 are significant.

Step4: Analyze number d (0.00003002)

Leading zeros are not significant, and zeros between non - zero digits are significant. 3, 0, 0, 2 are significant.

Step5: Analyze part 2a (0.000015045)

Leading zeros are not significant. There are 5 significant figures (1, 5, 0, 4, 5).

Step6: Analyze part 2b (4,600,000)

Trailing zeros without a decimal point may not be significant. There are 2 significant figures (4, 6).

Step7: Analyze part 2c (2406)

Zeros between non - zero digits are significant. There are 4 significant figures (2, 4, 0, 6).

Step8: Analyze part 2d (0.000005)

Leading zeros are not significant. There is 1 significant figure (5).

Step9: Analyze part 2e (0.0300001)

Leading zeros are not significant, and zeros between non - zero digits are significant. There are 6 significant figures (3, 0, 0, 0, 0, 1).

Step10: Analyze part 2f (12,000)

Trailing zeros without a decimal point may not be significant. There are 2 significant figures (1, 2).

Answer:

1.
a) Signficant digits: 4, 1, 8, 2
b) Signficant digits: 4, 9, 4, 1
c) Signficant digits: 3, 2, 0, 1
d) Signficant digits: 3, 0, 0, 2
2.
a) 5
b) 2
c) 4
d) 1
e) 6
f) 2