# Unit Conversion ad Significant Figures

• Soaring Crane
In summary, the conversation discusses unit conversion and significant figures in the context of various problem-solving scenarios. The first question involves calculating the mass in tons of antifreeze added to a car's radiator, while considering the number of significant figures. The second question revolves around the speed of a running back and how it can be converted to a different unit of measurement, also considering significant figures. The third question involves determining the time a vehicle has before running out of fuel, again considering significant figures. Lastly, the conversation touches on finding the number of atoms in a line on a piece of paper, using significant figures in calculations.
Soaring Crane
Unit Conversion & Significant Figures

Greetings! I would just like to re-check my work:

1) What will be the mass in tons added to a car when its radiator is filled with antifreeze (d = 1.12 g/mL) if the radiator has a capacityof 3.99 gal?

Since density = mass/volume, mass = density*volume. So I change 3.99 gal into L and then mL. After I solve for mass, the answer is in grams, so I convert to tons (g -> kg -> ton). The number of sig. figs. is 3?

2) A running back in Europe lists his speed as 6.0 s for 31 m. How fast can he run 48 yds?

First, change 31 m -> yds. Now speed = distance/time. For time = distance/speed = [48 yds]/[(31m*1.0936 yd)/(6.0 s)]. Number of sig. figs. is 2?

3) A vehicle traveling at 57 mi per hr. has a fuel consumption of 18.6 mi per gal. If vechicle is carrying 5.3 gal of gasoline, how many min. does the driver have before vehicle runs out of fuel?

speed = 57 mi/hr; consumption = 18.6 mi/gal

18.6 mi/gal *5.3 gal = amt. of mi able to travel = distance, so time = distance/speed = (98.58 mi)/(57 mi/hr) = time in hr. -> convert to min ?

Number of sig. figs. is 2?

4) Diameter of C atom found in Pb of pencil is 0.15 nm. Suppose a line is drawn on piece of paper that has width of 0.330 mm, length of 52.000 mm, and thickness of 0.010 mm, determine number of atoms in that line.

First find Volume of line by l*w*h = mm^3, and covert to m^3 where 1 m^3 = (1000 mm)^3. Convert nm to m (0.15 nm*(1m/10^9 nm)). Now divide C atom's diameter by 2 for radius to use V = (4/3)*pi*r^3. Divide V of line/V of 1 C atom. Number of sig. figs. is 2?

Thank you.

Last edited:
Try this tutorial on significant digits.

http://ist-socrates.berkeley.edu/~chem1a/sigfigs/sigfig2.htm

Last edited by a moderator:

Hello! Your calculations and conversions seem correct. Let's go through each problem to check the significant figures.

1) The answer for mass should be rounded to 3 significant figures since the given values (density and volume) are only given to 3 significant figures.

2) The answer for speed should also be rounded to 3 significant figures since the given values (distance and time) are only given to 3 significant figures.

3) The answer for time should be rounded to 2 significant figures since the given values (speed and consumption) are only given to 2 significant figures.

4) The answer for the number of atoms should be rounded to 2 significant figures since the given values (length, width, and thickness) are only given to 2 significant figures.

Overall, your conversions and calculations are correct, but make sure to pay attention to the number of significant figures in the given values to determine the correct number of significant figures in your final answer. Keep up the good work!

## 1. What is unit conversion and why is it important?

Unit conversion is the process of converting a quantity from one unit of measurement to another. It is important because it allows us to compare and communicate measurements that are in different units, making it easier to understand and work with data.

## 2. How do I convert between different units of measurement?

To convert between units, you need to know the conversion factor, which is the relationship between the two units. You can then multiply the original value by the conversion factor to get the converted value. It is important to pay attention to the units and make sure they cancel out, leaving you with the desired unit in the end.

## 3. What are significant figures and why are they important in measurement?

Significant figures are the digits in a number that carry meaning and contribute to the precision of the measurement. They are important because they indicate the level of uncertainty in a measurement. The more significant figures, the more precise the measurement is considered to be.

## 4. How do I determine the number of significant figures in a measurement?

In general, all non-zero digits are considered significant. Zeros at the beginning of a number are not significant, but zeros in between or at the end of a number are significant. To determine the number of significant figures, count all the non-zero digits and any final zeros after the decimal point.

## 5. How do I round a measurement to the correct number of significant figures?

When rounding a measurement, you should first determine the desired number of significant figures. Then, starting from the left, identify the first non-zero digit and keep all digits to the right. If the digit to the right is 5 or greater, round up the previous digit. If it is less than 5, leave the previous digit unchanged. Any final zeros after the decimal point should be kept if they are significant, otherwise they can be dropped.

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