Question

Use dimensional analysis to convert 4.30 days to seconds. (Hint: Don’t forget about the significant figures)
A. 258 seconds
B. 929,000 seconds
C. 15,000 seconds
D. 372,000 seconds
E. 6,190 seconds

Answer 1

Hint: During our day-to-day calculations there is a need for conversion. Sometimes we need to convert from one system of representation to another. The method used for this is called dimensional analysis. Dimensional analysis is also known as the factor label method or unit factor method.

Complete step by step answer:
Significant figures are meaningful digits that are known with certainty. The uncertainty is indicated by writing the certain digits and the last digit as an uncertain digit. Unless stated the uncertainty associated with the last digit is $ \pm 1$ .
In the question above 4.30 days are to be converted into seconds. Here the representation of the number of days contains 3 significant digits as the zero after the decimal and all the non-zero digits are considered significant.
As the number of days has 3 significant digits, the converted value must also have the same number of significant digits (3 in this case)
Given number of days = 4.30
Number of hours in a day = 24 hours
Number of minutes in an hour = 60 minutes
Number of seconds in a minute = 60 seconds
Therefore to calculate the number of seconds in a given number of days we need to use the relations specified above.
So, ${\text{Number of seconds in 4..30 days} = \text{Number of hours in 4.30 days }} \times {\text{ Number of minutes in an hour }} \times {{ Number of seconds in a minute }}$
$ \Rightarrow {\text{Number of hours = (4}}{{.30 }} \times {{ 24) }} \times {{ 60 }} \times {{ 60}}$
$ \Rightarrow {\text{Number of hours = 371,520}}$
Since the original value had 3 significant digits so the final value must also have 3 significant digits and our answer has 5 significant digits we need to round it off to 3 significant digits
So, rounding off to 3 significant digits 371,520 $ \approx $ 372000
Since the trailing zeros after a non-zero digit on the left side of the decimal are non-significant thus 372,000 has 3 significant digits.

So, the correct answer is Option D.

Note: There are certain rules for determining the significant figures as stated below
All nonzero digits are significant
Zero before he first nonzero digit are non-significant
Zero between two nonzero digits are significant
Zeroes on the right of the non-zero and after the decimal point are significant
Counting numbers of objects have infinite significant digits.