To what decimal place should each answer be rounded? and how many significant figures does the rounded answer have?
a) 9cm + 2.8 cm= 11.8cm (unrounded)
b) 0.135 atm + 0.6 atm= 0.735 atm (unrounded)
can you show me how to do this?
Read significant figures and rounding here.
http://www.chemteam.info/SigFigs/SigFigs.html
To determine to what decimal place each answer should be rounded and the number of significant figures in the rounded answer, we need to consider the values and rules for adding or adding measurements with different precisions.
a) 9cm + 2.8 cm = 11.8 cm (unrounded)
To determine the decimal place to which the answer should be rounded, we look at the least precise measurement, which is 2.8 cm in this case. Since this measurement is precise to the nearest tenth of a centimeter (1 decimal place), the answer should also be rounded to this decimal place.
Now, let's consider the significant figures. The number 9 has one significant figure, while 2.8 has two significant figures. When adding or subtracting measurements, the result should have the same number of decimal places as the least precise measurement. However, the number of significant figures is determined by the least number of significant figures among the measurements being added. In this case, the least number of significant figures is one (from the number 9). Therefore, the rounded answer should have one significant figure.
Rounding the unrounded answer (11.8 cm) to one decimal place and one significant figure, we get the rounded answer of 10 cm.
b) 0.135 atm + 0.6 atm = 0.735 atm (unrounded)
To determine the decimal place to which the answer should be rounded, we again look at the least precise measurement, which is 0.135 atm. This measurement is precise to the thousandth place (3 decimal places), so the answer should also be rounded to this decimal place.
Regarding the significant figures, 0.135 atm has three significant figures, while 0.6 atm has one significant figure. When adding or subtracting measurements, the result should have the same number of decimal places as the least precise measurement. However, the number of significant figures is determined by the least number of significant figures among the measurements being added. In this case, the least number of significant figures is one (from 0.6 atm). Therefore, the rounded answer should have one significant figure.
Rounding the unrounded answer (0.735 atm) to three decimal places and one significant figure, we get the rounded answer of 0.700 atm.