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.

1. the measurement 0.0255 g, rounded off to two significant figures, would be

a. 0.02 g.
b. 0.025 g.
c. 0.026 g.
d. 2.5 x 10² g.

1. what is 1 x 10² divided by 1 x 10³?

a. 1 x 10⁶
b. 1 x 10⁻¹
c. 1 x 10⁵
d. 1 x 10⁵

1. 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 x 10² g
b. 1.0 x 10² g
c. 1.000 x 10² g
d. 1.00 x 10² g

1. 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

1. 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?

1. if you divide a samples mass by its density, what are the resulting units?

Explanation:

Step1: Recall significant - digit rules

Non - zero digits are always significant. Leading zeros (zeros before non - zero digits) are not significant. Zeros between non - zero digits are significant. Trailing zeros are significant only if there is a decimal point.

Step2: Answer question 30

Based on the rules, all non - zero digits are significant. So the answer is b.

Step3: Answer question 31

For 0.0255 g, the first non - zero digits are 2 and 5. To round to two significant figures, we look at the third digit (5). Since 5 is 5 or greater, we round up the second significant digit. So 0.0255 g rounded to two significant figures is 0.026 g. The answer is c.

Step4: Answer question 32

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

Step5: Answer question 33

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

Step6: Answer question 34

Accuracy is defined as how close a measured value is to the accepted value. So a measured quantity has good accuracy if it agrees closely with the accepted value. The answer is a.

Step7: Answer 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 \(4.00\div7.0\) is correct for calculating density. So the answer is yes.

Step8: Answer question 35b

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

Step9: Answer question 36

The density formula is \(
ho=\frac{m}{V}\), so \(V=\frac{m}{
ho}\). The units of mass are grams (g) and the units of density are \(g/mL\). So \(g\div(g/mL)=mL\). The resulting units are milliliters (mL).

Answer:

1. b. all non - zero digits are significant.
2. c. 0.026 g
3. b. \(1\times10^{-1}\)
4. c. \(1.000\times10^{2}\ g\)
5. a. it agrees closely with the accepted value.
6. a. Yes

b. 2

1. mL