Question

recap/review 3.1 and 3.2 ws

1. if the accepted value is 8.8 and experimental is 4.9. calculate % error? ans.

solve the following problems. write the answer your calculator gives you. then, write down the answer using correct significant figures. dont forget units!

	calculator answer	answer w/ sig. figs
a)	3.45 cm + 3.4 cm	6.85 cm	6.9 cm
b)	3.43 cm - 0.056 cm	3.374 cm	3.37 cm
c)	8.4 m / 10 m
a)	5.43 g x 3.4 g
b)	8.001 m x 2.3 s
c)	800 cm x 6.45 s
d)	6.00 g / 0.05 ml =
e)	5.01 g / 1.002000 molecules =

round 742,396 to four, three, and two significant digits:
a) four significant digits
b) three significant digits
c) two significant digits
round 0.07284 to four, three, and two significant digits:
a) four significant digits
b) three significant digits
c) two significant digits

Explanation:

Step1: Calculate percentage - error formula

The formula for percentage - error is $\text{Percent Error}=\frac{\vert\text{Experimental Value}-\text{Accepted Value}\vert}{\text{Accepted Value}}\times100\%$. Given that the accepted value is $8.8$ and the experimental value is $4.9$. First, find the difference: $\vert4.9 - 8.8\vert=\vert- 3.9\vert = 3.9$.

Step2: Calculate percentage - error

Then, substitute into the formula: $\text{Percent Error}=\frac{3.9}{8.8}\times100\%$. $\frac{3.9}{8.8}\approx0.44318$, and $0.44318\times100\% = 44.318\%\approx44\%$.

a)

Step1: Addition of measurements

For $3.45\text{ cm}+3.4\text{ cm}$, on a calculator, $3.45 + 3.4=6.85\text{ cm}$. When adding measurements, we round to the least number of decimal places. $3.4$ has one decimal place, so the answer with correct significant - figures is $6.9\text{ cm}$.

b)

Step1: Subtraction of measurements

For $3.43\text{ cm}-0.056\text{ cm}$, on a calculator, $3.43-0.056 = 3.374\text{ cm}$. Since $3.43$ has two decimal places, the answer with correct significant - figures is $3.37\text{ cm}$.

c)

It seems the operation for $8.4\text{ m}\ 10\text{ m}$ is not clear. Assuming it's a subtraction $8.4\text{ m}-10\text{ m}=- 1.6\text{ m}$ (calculator answer), and with correct significant - figures (one decimal place as in $8.4$) it's $-1.6\text{ m}$.

d)

Step1: Multiplication of measurements

For $5.43\text{ g}\times3.4\text{ g}$, on a calculator, $5.43\times3.4 = 18.462\text{ g}^2$. When multiplying, we consider significant figures. $3.4$ has two significant figures, so the answer with correct significant - figures is $18\text{ g}^2$.

e)

Step1: Multiplication of measurements

For $8.001\text{ m}\times2.3\text{ s}$, on a calculator, $8.001\times2.3=18.4023\text{ m}\cdot\text{s}$. Since $2.3$ has two significant figures, the answer with correct significant - figures is $18\text{ m}\cdot\text{s}$.

f)

Step1: Multiplication of measurements

For $800\text{ cm}\times6.45\text{ s}$, on a calculator, $800\times6.45 = 5160\text{ cm}\cdot\text{s}$. Since $800$ has one significant figure (if it's not an exact number), the answer with correct significant - figures is $5000\text{ cm}\cdot\text{s}$.

g)

Step1: Division of measurements

For $6.00\text{ g}/0.05\text{ ml}$, on a calculator, $\frac{6.00}{0.05}=120\text{ g/ml}$. Since $0.05$ has one significant figure, the answer with correct significant - figures is $100\text{ g/ml}$.

h)

Step1: Division of measurements

For $5.01\text{ g}/1.002000\text{ molecules}$, on a calculator, $\frac{5.01}{1.002000}=5.00\text{ g/molecule}$ (rounded to three significant figures as $5.01$ has three significant figures).

Rounding 742396:

a)

Step1: Four significant figures

To four significant figures, we look at the fifth digit. The number is $742396$. The fifth digit is $9$. Since $9\geq5$, we round up the fourth digit. So, $742400$.

b)

Step1: Three significant figures

To three significant figures, we look at the fourth digit. The fourth digit is $3$. Since $3\lt5$, we keep the first three digits as they are. So, $742000$.

c)

Step1: Two significant figures

To two significant figures, we look at the third digit. The third digit is $2$. Since $2\lt5$, we keep the first two digits as they are. So, $740000$.

Rounding 0.07284:

a)

Step1: Four significant figures

The number is already $0.07284$ with four significant figures (the leading zeros are not significant). So, $0.07284$.

b)

Step1: Three significant figures

We look at the fourth digit. The fourth digit is $4$. Since $4\lt5$, we keep the first three non - zero digits. So, $0.0728$.

c)

Step1: Two significant figures

We look at the third digit. The third digit is $8$. Since $8\geq5$, we round up the second digit. So, $0.073$.

Answer:

1. Percent Error: $44\%$

a) Calculator answer: $6.85\text{ cm}$, Answer with sig. figs: $6.9\text{ cm}$
b) Calculator answer: $3.374\text{ cm}$, Answer with sig. figs: $3.37\text{ cm}$
c) Assuming subtraction, Calculator answer: $-1.6\text{ m}$, Answer with sig. figs: $-1.6\text{ m}$
d) Calculator answer: $18.462\text{ g}^2$, Answer with sig. figs: $18\text{ g}^2$
e) Calculator answer: $18.4023\text{ m}\cdot\text{s}$, Answer with sig. figs: $18\text{ m}\cdot\text{s}$
f) Calculator answer: $5160\text{ cm}\cdot\text{s}$, Answer with sig. figs: $5000\text{ cm}\cdot\text{s}$
g) Calculator answer: $120\text{ g/ml}$, Answer with sig. figs: $100\text{ g/ml}$
h) Calculator answer: $5.00\text{ g/molecule}$, Answer with sig. figs: $5.00\text{ g/molecule}$
Rounding 742396:
a) $742400$
b) $742000$
c) $740000$
Rounding 0.07284:
a) $0.07284$
b) $0.0728$
c) $0.073$