University:
University of Arkansas
Course:
CHEM 1053 | Chemistry in the Modern World
Academic year:

2023
Views:

280

Pages:

1
Author:

madeleinejames20

In this example problem, we will keep track of significant figures in calculations. The first thing we'll want to do is plug this into our calculator to determine a numerical answer. Plugging it into your calculator, you should get 1000. Unfortunately, a standard calculator can't keep track of significant figures, so we'll have to follow the rules for significant figures to determine how many our answer should have. Following the order of operations, the first thing we'll want to do is determine how many significant figures are in the numerator. Whenever I do addition or subtraction, I like to line up all of the numbers with respect to their decimal points. This makes it easier to keep track of the significant figures in the calculation. The rule for significant figures in addition and subtraction is that our result will only be as significant as our least significant number with respect to the decimal point. In this case, with respect to the decimal point, our least significant number is in the ones column. So the significant figures in our result should only be carried as far as the ones column. That means that this number has four significant figures. Next in our order of operations, we can determine how many significant figures the denominator has. To determine the number of significant figures we should keep in our result, we can look at the number with the least significant digits with respect to the decimal point. In this case, our least significant number is limited to the hundredths column or two numbers past the decimal point. So our result should only carry three significant figures. Now, with the order of operations, we can do our division. We have a number with four significant figures being divided by our number with three significant figures. In multiplication or division, our result carries the same number of significant figures as the factor with the fewest significant figures. So our answer should only have three significant figures. In order to communicate that we want three significant figures for the number 1000, we'll need to convert the number into scientific notation. So to convert 1000 into scientific notation, we'll have to move the decimal point to the right or the left until we get a number that's between 1 and 9.999 (repeating). In this case, we'll move the decimal place to the left once, twice, three times, so that our answer should be 1.00 x 10^3. Our coefficient, 1.00, has three significant figures.