1. Subtleties of significant figures. Circle the phrase (or value) that makes th
ID: 713875 • Letter: 1
Question
1. Subtleties of significant figures. Circle the phrase (or value) that makes the statement correct.
a. For addition and subtraction, keep the ( maximum / minimum ) number of ( decimal places / significant figures ).
b. For multiplication and division, keep the ( maximum / minimum ) number of ( decimal places / significant figures ).
c. Leading zeroes, such as those found in 0.0000033, ( do / do not ) count as significant figures.
d. Trailing zeroes, such as those found in 33000, ( do / do not ) count as significant figures.
e. Trailing zeroes, such as those found in 330.0, ( do / do not ) count as significant figures.
f.
The value 0.002500 has ( 2 / 4 / 5 / 7 ) significant figures.
g. The value 4.550×10
8
has ( 3 / 4 / 8 / 9 ) significant figures.
h. The number of sig figs in log ( 1.81×10
-15
) is ( 1 / 2 / 3 / 4 / 15 / 16 / 17 ) – only the 1.81 portion is significant
i.
When the value 7.15 is rounded to two significant figures, the result is ( 7.1 / 7.2 ). – Tricky! When dropping only a
“5”, round to the nearest EVEN value.
j.
When the value 7.25 is rounded to two significant figures, the result is ( 7.2 / 7.3 ). –Tricky!
Explanation / Answer
Some of the rules that one must consider for assinging number of significant figures are:-
1. Non zero numbers are always significant.
2. Zeroes trapped in between two non zero numbers are always significant. Ex- The two zeroes in 8002 are significant.
3. Leading zeroes are never significant.
4. Trailing zeroes are significant only if there is a decimal point in the number. Ex- 70000 has only one significant figure but 70000.00 has 7 significant figures; due to the presence of a decimal, all zeroes become significant.
5. 10 raise to power something is never significant.
Considering these rules, I am writing the correct statements:-
a. For addition and subtraction, keep the minimum number of decimal places.
b. For multiplication and division, keep the minimum number of significant figures.
c. Leading zeroes, such as those found in 0.0000033, do not count as significant figures.
d. Trailing zeroes, such as those found in 33000,do not count as significant figures.
e. Trailing zeroes, such as those found in 330.0, do count as significant figures.
f.The value 0.002500 has 4 significant figures.
g. The value 4.550×108 has 4 significant figures.
h. The number of sig figs in log ( 1.81×10-15) is 5. The rule is that the number of significant figures in the number of which the log is taken should be equal to the number of significant figures in mantissa (Mantissa is the decimal part of the number). So log(1.81*10-15) gives -14.74232 as the answer but the original number has only three significant figures so the answer will have 3 decimal places. Hence the answer becomes -14.742 which has 5 significant figures.
i.When the value 7.15 is rounded to two significant figures, the result is 7.2
j.When the value 7.25 is rounded to two significant figures, the result is 7.2
For rounding off a 5, if the number preceding 5 is an odd number, increase it by 1. Therefore, 7.15 becomes 7.2
If the number preceding 5 is an even number then just drop the 5 without increasing the preceding number. Therefore, 7.25 also becomes 7.2
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