Question

1.2 measurements in chemistry
perform the following arithmetic and round off the answer to the correct number of significant figures. (47.346 - 47.312)/(7.42 x 1.56)
○ 0.0029
○ 0.003
● 0.00294
○ 0.002941

Explanation:

Step1: Calculate the numerator

First, we calculate the subtraction in the numerator: \(47.346 - 47.312 = 0.034\)

Step2: Calculate the denominator

Next, we calculate the multiplication in the denominator: \(7.42\times1.56 = 11.5752\)

Step3: Divide numerator by denominator

Now, we divide the result of the numerator by the result of the denominator: \(\frac{0.034}{11.5752}\approx0.002937\)

Step4: Determine significant figures

For addition/subtraction, the result should have the same number of decimal places as the least precise measurement. In \(47.346 - 47.312\), the least number of decimal places is 3, so the result \(0.034\) has 2 significant figures (the leading zeros don't count, the 3 and 4 are significant). For multiplication/division, the result should have the same number of significant figures as the least precise measurement. In \(7.42\times1.56\), \(7.42\) has 3 significant figures and \(1.56\) has 3 significant figures, so the product has 3 significant figures. When we divide \(0.034\) (2 significant figures) by \(11.5752\) (3 significant figures), the result should have 2 significant figures. Rounding \(0.002937\) to 2 significant figures gives \(0.0029\) (the first non - zero digit is 2, the next digit is 9, and we look at the next digit 3 which is less than 5, but wait, actually when rounding \(0.002937\) to two significant figures, we consider the 2 and 9. The number is \(2.937\times 10^{- 3}\), rounding to two significant figures gives \(2.9\times10^{-3}=0.0029\))

Answer:

0.0029