directions: use the graph to answer the questions
graph: solubility vs. temperature, with potassium nitrate, lines a-e, temperature (°c) 0-100, solubility (g/100g water) 0-100
14b (unit 1)
b. what is the independent variable?
c. what is the dependent variable?
d. what happens to the solubility of potassium nitrate as temperature increases?
4 • measurements and significant figures
image: balance with a cup
a. what would you need to do to get the mass of the coffee inside the cup?
b. what piece of laboratory equipment would you need to get the volume of the coffee in the cup?
determine the number of significant digits in each of the following and underline the estimated digit:
c. 717 ______ d. 0.150 ______ e. 0.0750 ______ f. 5000 ______ g. 50. ______
h. what do the number of significant digits tell us about a measurement?
5 • calculations and rounding to sig figs
a. calculate the density of an unknown substance with a mass of 8.10g and a volume of 2.3ml. use correct sig figs and units.

Question

Accepted Answer

### Part 4: Measurements and Significant Figures

#### c. 717
# Explanation:
## Step1: Identify significant digits
All non - zero digits are significant. In 717, the digits 7, 1, and 7 are all significant. The estimated digit (the last digit) is 7.
So the number of significant digits is 3, and we underline the last 7: $\underline{7}1\underline{7}$ (wait, actually, for a number like 717, the right - most digit is the estimated one. So we have 71$\underline{7}$. The number of significant digits is 3.
## Step2: Count the significant digits
Since all three digits (7, 1, 7) are significant, the number of significant digits is 3.
# Answer: 3, 71$\underline{7}$

#### d. 0.150
# Explanation:
## Step1: Identify significant digits
Leading zeros are not significant. Non - zero digits (1, 5) and the trailing zero after the decimal are significant. The estimated digit is the last zero (the trailing zero after the decimal).
## Step2: Count the significant digits
The significant digits are 1, 5, 0 (the trailing zero). So there are 3 significant digits. We underline the last 0: 0.15$\underline{0}$.
# Answer: 3, 0.15$\underline{0}$

#### e. 0.0750
# Explanation:
## Step1: Identify significant digits
Leading zeros are not significant. The non - zero digits 7, 5 and the trailing zero after the decimal are significant. The estimated digit is the last zero.
## Step2: Count the significant digits
The significant digits are 7, 5, 0 (the trailing zero). So there are 3 significant digits. We underline the last 0: 0.075$\underline{0}$.
# Answer: 3, 0.075$\underline{0}$

#### f. 5000
# Explanation:
## Step1: Identify significant digits
Trailing zeros in a whole number without a decimal are ambiguous, but if we consider that maybe the number is written as 5000. (with an implied decimal), or if it's known that the zeros are significant, but usually, for 5000, if we assume that the 5 is significant and the zeros may or may not be. But if we take it as having 1 significant digit (the 5) and the estimated digit is the last zero (but this is a bit ambiguous). However, if we consider that 5000 is written to show that the zeros are significant (maybe in a context where it's 5000. with a decimal), but as per the problem, we can assume that if it's 5000, and we are to find significant digits, the non - zero digit 5 is significant, and the zeros are placeholders. But maybe the problem considers 5000 as having 1 significant digit, and the estimated digit is the last 0. But another interpretation: if it's 5.000×10³, then it has 4 significant digits. But given the problem's context, let's assume the first case. Wait, maybe the problem expects us to consider that trailing zeros in a number without a decimal are not significant unless there is a decimal. So 5000 has 1 significant digit (5), and the estimated digit is the last 0. But this is a bit of a problem. Alternatively, if the number is 5000 with the intention that all zeros are significant (like 5000. with a decimal), then it has 4 significant digits. But since the problem says "underline the estimated digit", let's go with the first interpretation: 1 significant digit, estimated digit is the last 0. But maybe the problem expects 4? Wait, no. Let's check the rules: leading zeros not significant, trailing zeros in whole numbers without decimal: ambiguous. But in many cases, for a number like 5000, if we are to find significant digits, and there is no decimal, we consider only the non - zero digit as significant. So 1 significant digit, estimated digit is the last 0. But I think maybe the problem has a typo or expects 4. Wait, maybe it's 5000 with a decimal implied, so 5000. has 4 significant digits. Let's assume that. So the significant digits are 5, 0, 0, 0, and the estimated digit is the last 0. So number of significant digits is 4, and we underline the last 0: 500$\underline{0}$.
# Answer: 4, 500$\underline{0}$ (assuming the number is 5000. with an implied decimal)

#### g. 50.
# Explanation:
## Step1: Identify significant digits
The 5 and the 0 (because there is a decimal after the 0) are significant. The estimated digit is the 0.
## Step2: Count the significant digits
There are 2 significant digits. We underline the 0: 5$\underline{0}$.
# Answer: 2, 5$\underline{0}$.

#### h. What do the number of significant digits tell us about a measurement?
# Brief Explanations:
The number of significant digits in a measurement tells us about the precision of the measurement. More significant digits generally mean a more precise measurement, as they indicate the level of detail to which the measurement was made (including the estimated digit which shows the uncertainty in the last measured digit).
# Answer: The number of significant digits tells us the precision of the measurement (how detailed/accurate the measurement is, including the estimated digit's uncertainty).

### Part 5: Calculations and Rounding to Sig Figs

#### a. Calculate the density of an unknown substance with a mass of 8.10g and a volume of 2.3mL. Use correct sig figs and units.
# Explanation:
## Step1: Recall the density formula
The formula for density ($
ho$) is $
ho=\frac{m}{V}$, where $m$ is mass and $V$ is volume.
## Step2: Substitute the values
Substitute $m = 8.10\space g$ and $V=2.3\space mL$ into the formula: $
ho=\frac{8.10}{2.3}\space g/mL$.
## Step3: Perform the division
$\frac{8.10}{2.3}\approx3.5217\space g/mL$.
## Step4: Round to significant figures
The mass (8.10) has 3 significant digits, and the volume (2.3) has 2 significant digits. When dividing, the result should have the same number of significant digits as the least precise measurement (the one with the fewest significant digits). So we round to 2 significant digits.
$3.5217\approx3.5\space g/mL$ (wait, no: 8.10 has 3 sig figs, 2.3 has 2 sig figs. The rule for multiplication/division is that the result has the same number of sig figs as the quantity with the least number of sig figs. So 2 sig figs. $8.10\div2.3 = 3.5217\cdots\approx3.5\space g/mL$? Wait, 8.10 is 3 sig figs, 2.3 is 2 sig figs. So the answer should have 2 sig figs. Let's calculate 8.10/2.3: 8.10÷2.3 = 3.52173913... Rounding to 2 significant digits: look at the first two significant digits (3 and 5), the next digit is 2, which is less than 5, so we keep it 3.5? Wait, no, 3.5217, the first two significant digits are 3 and 5, the third is 2. So 3.5 (2 sig figs). Wait, but 8.10 is 3 sig figs, 2.3 is 2 sig figs. So the limiting factor is 2 sig figs. So the density is approximately $3.5\space g/mL$? Wait, no, 8.10 divided by 2.3: 8.10 has three significant figures, 2.3 has two. So the result should have two significant figures. Let's do the division more accurately: 8.10 ÷ 2.3. 2.3×3.5 = 8.05, 2.3×3.52 = 8.096, which is close to 8.10. So 3.52, but we need two significant figures. So 3.5? Wait, no, 3.5 has two significant figures. Wait, 3.52 rounded to two significant figures is 3.5? Wait, no, the first two significant digits are 3 and 5, the next digit is 2, which is less than 5, so we round down, so 3.5. But wait, 8.10 is 3 sig figs, 2.3 is 2 sig figs. So the answer should have 2 sig figs. So $
ho=\frac{8.10\space g}{2.3\space mL}\approx3.5\space g/mL$ (2 sig figs).
# Answer: The density is $\boldsymbol{3.5\space g/mL}$ (or $\boldsymbol{3.5\space g\cdot mL^{-1}}$)

### Part about the solubility graph (assuming the questions are b, c, d):

#### b. What is the independent variable?
# Brief Explanations:
In a solubility - temperature graph, the independent variable is the one that is manipulated or is the cause, which is temperature (in °C).
# Answer: Temperature (°C)

#### c. What is the dependent variable?
# Brief Explanations:
The dependent variable is the one that depends on the independent variable. In a solubility - temperature graph, solubility (in g/100g water) depends on temperature, so the dependent variable is solubility.
# Answer: Solubility (g/100g water)

#### d. What happens to the solubility of potassium nitrate as temperature increases?
# Brief Explanations:
From the graph (looking at the potassium nitrate curve), as temperature (x - axis) increases, the solubility (y - axis) of potassium nitrate increases (the curve for potassium nitrate has a positive slope, going up as temperature increases).
# Answer: The solubility of potassium nitrate increases as temperature increases.

### Part 4a and 4b:

#### 4a. What would you need to do to get the mass of the coffee inside the cup?
# Brief Explanations:
To find the mass of the coffee inside the cup, you can use the principle of subtraction. First, measure the mass of the empty cup (let's call it $m_{cup}$), then measure the mass of the cup with the coffee (let's call it $m_{cup + coffee}$). Then, the mass of the coffee ($m_{coffee}$) is $m_{coffee}=m_{cup + coffee}-m_{cup}$.
# Answer: Measure the mass of the empty cup and the mass of the cup with coffee, then subtract the mass of the empty cup from the mass of the cup with coffee (i.e., $m_{coffee}=m_{cup + coffee}-m_{cup}$).

#### 4b. What piece of laboratory equipment would you need to get the volume of the coffee in the cup?
# Brief Explanations:
To measure the volume of a liquid (coffee) in a cup, a graduated cylinder (or a volumetric flask, but a graduated cylinder is more common for this purpose) can be used. You can pour the coffee from the cup into a graduated cylinder and read the volume from the graduated markings on the cylinder.
# Answer: A graduated cylinder (or volumetric flask, but graduated cylinder is more typical for this task).

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Part 4: Measurements and Significant Figures

c. 717

Step1: Identify significant digits

Step2: Count the significant digits

Step1: Identify significant digits

Step2: Count the significant digits

Step1: Identify significant digits

Step2: Count the significant digits

Answer:

d. 0.150