Question

1. to determine the number of significant digits in a measurement, follow the rule that a. all zeros are significant. b. all nonzero digits are significant. c. zeros between digits are not significant. d. final digits less than 5 are not significant. 31. the measurement 0.0055 g, rounded off to two significant figures, would be a. 0.002 g b. 0.005 g c. 0.0055 g d. 2.5×10⁻³ g 32. what is 1×10⁵ divided by 1×10³? a. 1×10⁸ b. 1×10⁻² c. 1×10² d. 1×10³ 33. what is the sum of 100.0 g and 0.01 g, expressed in scientific notation and written with the correct number of significant figures? a. 10001×10⁰ g b. 1.0×10² g c. 1.0001×10² g d. 1.00×10² g 34. a measured quantity is said to have good accuracy if? a. it agrees closely with the accepted value b. repeated measurements agree closely c. it has a small number of significant figures d. all digits in the value are significant short answer 35. a certain sample with a mass of 4.00 g is found to have a volume of 7.0 ml. to calculate the density of the sample, a student entered 4.00÷7.0 on a calculator. the calculator display shows the answer as 0.571429. a. is the setup for calculating density correct? b. how many significant figures should the answer contain? 36. if you divide a sample’s mass by its density, what are the resulting units?

Explanation:

Step1: Analyze question 30

The number 0.0255 rounded to two significant - figures: Non - zero digits are significant. We look at the third digit after the decimal. Since it is 5, we round up the second digit. 0.0255 rounds to 0.026. But in scientific notation, it can be written as \(2.6\times10^{- 2}\). However, among the given options, the closest correct one considering the format is c. 0.026 g.

Step2: Analyze question 32

When dividing numbers in scientific notation \(a\times10^{m}\div b\times10^{n}\), we use the rule \(\frac{a}{b}\times10^{m - n}\). Here, \(a = 1\), \(b = 1\), \(m=5\), \(n = 2\). So, \(1\times10^{5}\div1\times10^{2}=\frac{1}{1}\times10^{5 - 2}=1\times10^{3}\). The answer is a. \(1\times10^{3}\).

Step3: Analyze question 33

First, add 100.0 g and 0.01 g: \(100.0+0.01 = 100.01\) g. In scientific notation, with the correct number of significant figures (4 significant figures as 100.0 has 4 significant figures), it is \(1.0001\times10^{2}\approx1.000\times10^{2}\) g. The answer is c. \(1.000\times10^{2}\) g.

Step4: Analyze question 34

Accuracy is defined as how close a measured value is to the accepted value. Precision is about how close repeated measurements are to each other. A measured quantity has good accuracy if it agrees closely with the accepted value. The answer is a. it agrees closely with the accepted value.

Step5: Analyze question 35a

The density formula is \(
ho=\frac{m}{V}\), where \(m\) is mass and \(V\) is volume. Given \(m = 4.00\) g and \(V = 7.0\) mL, the setup \(4.00\div7.0\) on the calculator for density calculation is correct.

Step6: Analyze question 35b

For multiplication and division, the result should have the same number of significant figures as the number with the fewest significant figures in the values used in the calculation. 4.00 has 3 significant figures and 7.0 has 2 significant figures. So the answer should have 2 significant figures.

Step7: Analyze question 36

The density formula is \(
ho=\frac{m}{V}\), where the units of density \(
ho\) are \(\text{g/mL}\), mass \(m\) is in grams (\(\text{g}\)) and volume \(V\) is in milliliters (\(\text{mL}\)). If we divide mass \(m\) by density \(
ho\) (\(\frac{m}{
ho}\)), since \(
ho=\frac{m}{V}\), then \(\frac{m}{
ho}=V\). The units of volume are milliliters (\(\text{mL}\)) or cubic centimeters (\(\text{cm}^3\)).

Answer:

1. c. 0.026 g
2. a. \(1\times10^{3}\)
3. c. \(1.000\times10^{2}\) g
4. a. it agrees closely with the accepted value

35a. Yes
35b. 2

1. \(\text{mL}\) or \(\text{cm}^3\)