(\(a\)) When the calculation \((0.0043)(0.821)(298)\) is performed, the answer should be reported to___?___ significant figures. (\(b\)) The quotient (237.33)/(343) should be written with___?___ significant figures. (c) How many digits after the decimal point should be reported when the calculation \((199.0354 + 43.09 + 121.2)\) is performed?

(\(a\)) When the calculation \((0.0043)(0.821)(298)\) is performed, the answer should be reported to___?___ significant figures. (\(b\)) The quotient (237.33)/(343) should be written with___?___ significant figures. (c) How many digits after the decimal point should be reported when the calculation \((199.0354 + 43.09 + 121.2)\) is performed?

Solution:- Multiplication of \((0.0043)(0.821)(298)\) is \(1.0520\), Which could be written as \(1.05\) and by rounding off \(1.1\). Hence there are \(2\)- Significant figures

Explanation:- When multiplying or dividing, the number of significant figures is equal to the number of significant figures in the measurement with the fewest significant numbers. The lowest term in this multiplication result of \((0.0043)(0.821)(298)\), only has two significant figures. Consequently, the overall number of meaningful figures in the result is being limited by 2 hence the answer is \(2\)- Significant figures.

(\(b\)) The quotient (237.33)/(343) should be written with___?___ significant figures.

Solution:- In the the given fraction number \((\frac{237.33}{343})\) \(237.33\) has four significant figures, the number 343 has three significant digits that limits the result therefore, the answer should have only three significant figures. The calculation is \(0.69192\), Which could be rounded off to \(0.692\) or could also be written as in terms of power \(6.92\times10^{-1}\)

(\(c\)) How many digits after the decimal point should be reported when the calculation\((199.0354 + 43.09 + 121.2)\) is performed?

Solution:- For addition and subtraction, the limiting term is the one with the smallest number of decimal places. Out of given set of numbers in the question \(121.2\) having least number of significant figures which is \(3\) so that the number obtained after the addition would have \(3\) significant digits. The sum of \((199.0354 + 43.09 + 121.2)\) is equal to \(363.3254\) that could also be written as \(363\).