Question

the cylinder shown at right, the correct volume is 56.0ml. data table experiment 1 1) report how many significant figures each of the following numbers has and then write the number in standard scientific notation.
number\tnumber of significant figures\tstandard scientific notation
0.000062\t\t
0.0560\t\t
820.0\t\t

1. solve each of the following problems. report the final answer to the correct significant figures.

conversion factors:
1 oz = 29.57 ml\t453.6 g = 1 lb\t2.54 cm = 1 in
a) convert 52.30 ounces to milliliters. \t__________milliliters
b) convert 52 cm to in. \t__________inches
c) convert 16.90 lbs. to grams. \t__________grams
d) add 140.567 to 12.209 then divide this answer by 13.0 \t__________

Explanation:

Part 1: Significant Figures and Scientific Notation

For 0.000062:

Step1: Count significant figures

Leading zeros are not significant. The non - zero digits 6 and 2 are significant. So, the number of significant figures is 2.

Step2: Convert to scientific notation

We move the decimal point to the right of the first non - zero digit (6). We moved the decimal 5 places to the right. So, in scientific notation, it is $6.2\times10^{-5}$.

For 0.0560:

Step1: Count significant figures

Leading zeros are not significant. The digits 5, 6 are significant, and the trailing zero after the non - zero digit is also significant (because there is a decimal point). So, the number of significant figures is 3.

Step2: Convert to scientific notation

Move the decimal point to the right of 5. We moved it 2 places to the right. So, it is $5.60\times10^{-2}$.

For 820.0:

Step1: Count significant figures

All the digits 8, 2, 0 (the trailing zero after the decimal) are significant. So, the number of significant figures is 4.

Step2: Convert to scientific notation

Move the decimal point to the right of 8. We moved it 2 places to the right. So, it is $8.200\times10^{2}$.

Part 2: Unit Conversions and Calculations

a) Convert 52.30 ounces to milliliters

Step1: Use the conversion factor

The conversion factor is $1\ oz = 29.57\ mL$. So, to convert ounces to milliliters, we multiply the number of ounces by the conversion factor.
The formula is $Volume\ (mL)=52.30\ oz\times\frac{29.57\ mL}{1\ oz}$

Step2: Calculate the value

$52.30\times29.57 = 52.30\times(30 - 0.43)=52.30\times30-52.30\times0.43 = 1569-22.489 = 1546.511\ mL$. Considering significant figures, 52.30 has 4 significant figures and 29.57 has 4 significant figures. The result should have 4 significant figures. So, $1.547\times 10^{3}\ mL$ (or 1547 mL).

b) Convert 52 cm to in

Step1: Use the conversion factor

The conversion factor is $2.54\ cm = 1\ in$. So, $Length\ (in)=\frac{52\ cm}{2.54\ cm/in}$

Step2: Calculate the value

$\frac{52}{2.54}\approx20.47\ in$. 52 has 2 significant figures, so the result should have 2 significant figures. So, 20. in (or $2.0\times 10^{1}\ in$).

c) Convert 16.90 lbs. to grams

Step1: Use the conversion factor

The conversion factor is $453.6\ g = 1\ lb$. So, $Mass\ (g)=16.90\ lb\times\frac{453.6\ g}{1\ lb}$

Step2: Calculate the value

$16.90\times453.6 = 16.90\times(450 + 3.6)=16.90\times450+16.90\times3.6=7605 + 60.84 = 7665.84\ g$. 16.90 has 4 significant figures and 453.6 has 4 significant figures. So, the result is $7.666\times 10^{3}\ g$ (or 7666 g).

d) Add 140.567 to 12.209 then divide this answer by 13.0

Step1: Add the numbers

$140.567+12.209 = 152.776$

Step2: Divide by 13.0

$\frac{152.776}{13.0}\approx11.752$. 140.567 has 6 significant figures, 12.209 has 5 significant figures, and 13.0 has 3 significant figures. When dividing, the result should have 3 significant figures. So, 11.8.

Filling the Table for Part 1:

Number	Number of Significant Figures	Standard Scientific Notation
0.0560	3	$5.60\times10^{-2}$
820.0	4	$8.200\times10^{2}$

Answer:

s for Part 2:

a) $\boldsymbol{1547}$ (or $1.547\times 10^{3}$) milliliters

b) $\boldsymbol{20.}$ (or $2.0\times 10^{1}$) inches

c) $\boldsymbol{7666}$ (or $7.666\times 10^{3}$) grams

d) $\boldsymbol{11.8}$