Conversion Factors Part 2: Single Step What if we didn't want The procedure to use the Dimensional Analysis calculator is as follows: Step 1: Enter two physical quantities in the respective input field. I don't t. It is often the case that a quantity of interest may not be easy (or even possible) to measure directly but instead must be calculated from other directly measured properties and appropriate mathematical relationships. It is great because is shows the relationship between the units. The equation relating the temperature scales is then: \[\mathrm{\mathit{T}_{^\circ F}=\left(\dfrac{9\:^\circ F}{5\:^\circ C}\times \mathit{T}_{^\circ C}\right)+32\:^\circ C} \nonumber \]. One gallon is 3.79 liters (1 gal = 3.79 liters). Does anyone know a better way of explaining what he's talking about? (from a complete OLI stoichiometry course) Dimensional analysis allows us to change the units used to express a value. We're done. Your cruise ship is leaving for a 610-league adventure. bit of too much overhead "to worry about when I'm just doing "a simple formula like this." The following video gives a brief overview of . Posted 5 years ago. Learn how to solve single-step and multi-step problems using dimensional analysis and understand the cancellation of units in a numerator and denominator. 1: One centimeter cubed is the volume occupied by a cube with an edge length of 1 cm . It shows the metric units for length, capacity, and mass. When we treated the units \u0026 Dimensional Analysis General Physics - Conversion of Units Examples Shortcut for Metric Unit Conversion PLTW IED - Unit Conversion 3.2 Notes . This is typically accomplished by measuring the time required for the athlete to run from the starting line to the finish line, and the distance between these two lines, and then computing speed from the equation that relates these three properties: \[\mathrm{speed=\dfrac{distance}{time}} \nonumber \], An Olympic-quality sprinter can run 100 m in approximately 10 s, corresponding to an average speed of, \[\mathrm{\dfrac{100\: m}{10\: s}=10\: m/s} \nonumber \]. 5. These calculations are examples of a versatile mathematical approach known as dimensional analysis (or the factor-label method). In this section, you will look at common unit conversions used in science. Legal. It is important to identify the given and the desired quantities in any problem. To determine the units of this quantity, we cancel the kilograms water Since a cm 3 is equal to a mL, and a dm 3 is equal to a L, we can say that there are 1000 mL in 1 L. Example 2.3. 1 kilogram over 1000 grams is equal to 1. . These calculations are examples of a versatile mathematical approach known as dimensional analysis (or the factor-label method). Step 2: Now click the button "Submit" to get the analysis. Type the correct answer in the box. But what I want to show you is that even with a simple formula like distance is equal to rate times time, what I just did could Several other commonly used conversion factors are given in Table \(\PageIndex{1}\). The units . use or teach dimensional analysis, work through the exercises in this chapter, paying . To convert from m 3 into units in the left column divide by the value in the right column or, multiply by the reciprocal, 1/x. 2. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. You may do simple problems like this frequently throughout the day. hours in the denominator and seconds in the numerator, times essentially seconds per hour. Notice how the dime units cancel out, leaving the dollar units in the answer. It might jump out of you, well, if we can get rid of this hours, if we can express it in terms of seconds, then that would cancel here, and we'd be left with just the meters, which is a unit of distance Dimensional analysis, or more specifically the factor-label method, also known as the unit-factor method, is a widely used technique for such conversions using the rules of algebra. Start with the given, 2,361 L. Direct link to elise's post In the practice, many of , Posted 4 years ago. We can convert any unit to another unit of the same dimension which can include things like time, mass . Alternatively, the calculation could be set up in a way that uses all the conversion factors sequentially, as follows: \[\mathrm{\dfrac{1250\:\cancel{km}}{213\:\cancel{L}}\times\dfrac{0.62137\: mi}{1\:\cancel{km}}\times\dfrac{1\:\cancel{L}}{1.0567\:\cancel{qt}}\times\dfrac{4\:\cancel{qt}}{1\: gal}=13.8\: mpg}\nonumber \]. Q: Calculate the pH of the resulting solution if 28.0 mL28.0 mL of 0.280 M HCl (aq)0.280 M HCl (aq) is. Thus, the volume in grams is equal to the liters multiplied by 1,000 times the density of the ingredient or material. The conversion factor of 1 cm 3 = 1 mL is a very useful conversion. equal to 5 meters per second, 5 meters per second times A commercial jet is fueled with 156,874 L of jet fuel. that we're familiar with. The trick with this way of doing the calculation is you have to remember to apply the power to EVERYTHING: $$\left ( \frac{1in}{2.54cm} \right )^{3}=\frac{\left ( 1^{3}in^{3} \right )}{2.54^{3}cm^{3}}$$. The mercury or alcohol in a common glass thermometer changes its volume as the temperature changes. Here's a chemistry problem. We need to use two steps to convert volume from quarts to milliliters. We're going to do our I am having difficulties applying what he said in the videos to the practice problems he's giving me. The process of manipulating our units is called dimensional analysis. use the correct number of significant figures for your final answer. Great question! Check Answer and/or View Worked out Solution. It shows you how perform conversions with SI units in the metric system and in the english system including units that contain exponents such as squares and cubes. This is the same thing as 5 times 10, 5 times 10 times meters per second, times meters per second times seconds, times seconds. Conversion factors allow us to convert from one unit (dimes) to another (dollars). Because the volume of the liquid changes more than the volume of the glass, we can see the liquid expand when it gets warmer and contract when it gets cooler. So how do we do that? Meave60. 2) Using the density of seawater, calculate the mass of seawater (in kilograms) in the oceans. $$5.70 L*\frac{1000 mL}{1 L}*\frac{1 cm^{3}}{1 mL}=5700cm^{3}$$. These conversions are accomplished using unit conversion factors, which are derived by simple applications of a mathematical approach called the factor-label method or dimensional analysis. Direct link to Nolan Ryzen Terrence's post There is nothing much to , Posted 6 years ago. For now, lets look at the following exercise that deals with setting up the conversion factors. Centiliter is 1/100 of a liter. In this section, we will be putting a lot of practice in learning to use the approach to solving chemical problems. Knowing that the conversion factor to get to molecules involves the number of mols, the first conversion you need to do from grams is to mol. 18- Oh, it's 18,000, 18,000, 18,000 meters. muscles a little bit more. What is that? Depending on the direction in which you are converting, this fact gives you a rate of conversion as either 1 inch for every 2.54 centimeters or 2.54 centimeters for every inch. x\:\ce{oz}&=\mathrm{125\:\cancel{g}\times \dfrac{1\: oz}{28.349\:\cancel{g}}}\\ The early 19th-century discovery of the relationship between a gas's volume and temperature suggested that the volume of a gas would be zero at 273.15 C. 50 lb/ft 3 * 16.018463 [ (kg/m 3) / (lb/ft 3) ] = 800.92315 kg/m 3. Knowing how to set up conversion factors, we can now move into setting up calculations using dimensional analysis, which is also known as the factor-label method. Alternatively, the calculation could be set up in a way that uses three unit conversion factors sequentially as follows: \[\mathrm{\dfrac{9.26\:\cancel{lb}}{4.00\:\cancel{qt}}\times\dfrac{453.59\: g}{1\:\cancel{lb}}\times\dfrac{1.0567\:\cancel{qt}}{1\:\cancel{L}}\times\dfrac{1\:\cancel{L}}{1000\: mL}=1.11\: g/mL}\nonumber \]. \end{align*} \nonumber \]. 500 grams to liter = 0.5 liter. The mass of a competition Frisbee is 125 g. Convert its mass to ounces using the unit conversion factor derived from the relationship 1 oz = 28.349 g (Table \(\PageIndex{1}\)). In this two-step method, we will covert as follows: microliters to liters and liters to milliliters. Road maps are very handy to use in doing calculations. Next we multiply by the ratio 1000 Grams can be abbreviated as g; for example, 1 gram can be written as 1 g. grams = liters 1,000 ingredient density, National Institute of Standards & Technology, Metric Cooking Resources, https://www.nist.gov/pml/owm/metric-cooking-resources, National Institute of Standards and Technology, Units outside the SI, https://physics.nist.gov/cuu/Units/outside.html. Dimensional Analysis is a powerful way to solve problems. We can do this by multiplying by the ratio 1000 milliliters of water over 1 liter of water. [4] Physical quantities that are commensurable have the same dimension; if they have different dimensions, they are incommensurable. The y-intercept of the equation, b, is then calculated using either of the equivalent temperature pairs, (100 C, 212 F) or (0 C, 32 F), as: \[\begin{align*} b&=y-mx \\[4pt] &= \mathrm{32\:^\circ F-\dfrac{9\:^\circ F}{5\:^\circ C}\times0\:^\circ C} \\[4pt] &= \mathrm{32\:^\circ F} \end{align*} \nonumber \]. Liters can be abbreviated as l, and are also sometimes abbreviated as L or . Most of us could have performed the calculation without setting up equivalences and conversion factors. Problem: A student needs 2,361 L of ethyl alcohol for an experiment. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. We use the word temperature to refer to the hotness or coldness of a substance. Lets take a closer look using this simple example to determine how many dollars equal 20 dimes. Consequently, converting a temperature from one of these scales into the other requires more than simple multiplication by a conversion factor, m, it also must take into account differences in the scales zero points (\(b\)). Watch the following videos. Direct link to Hedayat's post I'm doing this in my chem, Posted 3 years ago. The correct unit conversion factor is the ratio that cancels the units of grams and leaves ounces. Dimensional analysis is the process by which we convert between units and whether we should divide or multiply. To yield the sought property, time, the equation must be rearranged appropriately: \[\mathrm{time=\dfrac{distance}{speed}}\], \[\mathrm{\dfrac{25\: m}{10\: m/s}=2.5\: s}\], Again, arithmetic on the numbers (25/10 = 2.5) was accompanied by the same arithmetic on the units (m/m/s = s) to yield the number and unit of the result, 2.5 s. Note that, just as for numbers, when a unit is divided by an identical unit (in this case, m/m), the result is 1or, as commonly phrased, the units cancel.. [1][2][3]The concept of physical dimension was introduced by Joseph Fourier in 1822. &=\mathrm{\left(\dfrac{125}{28.349}\right)\:oz}\\ seconds, they give it in hours, so they say the time is equal to 1 hour. Please provide any two values to the fields below to calculate the third value in the density equation of. Dimensional Analysis Practice Problems. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Convert this to kilograms. Determine math problem . A liter is a unit of volume equal to 1,000 cubic centimeters. The gram, or gramme, is an SI unit of weight in the metric system. For now we will focus on single step conversions. This unit definition Figure 2.3. doing is actually called dimensional analysis. For example, 1 liter can be written as 1 l, 1 L, or 1 . Instead of giving it in Dont ever think that this approach is beneath you. When building a conversion factor for units raised to a power, we simply raise the conversion factor to the power we want our final units in. Free online density converter - converts between 42 units of density, including kilogram/cubic meter, gram/cubic centimeter, kilogram/cubic centimeter, gram/cubic meter [g/m^3], etc. Wikipedia, The Free Encyclopedia, 15 Jun. This is good practice for the many problems you will encounter in this and future chemistry and science courses. 1 gram = 1000 mg. 1 pound = 453.59 grams. The trick is to remember to raise the QUANTITY and UNITS by the power. can treat the units, as I've just said, like These are the units I will use. of your quantities correctly and prevent you from making mistakes in your computations. Metric Units \u0026 Unit Conversions Page 5/25. This method can be applied to computations ranging from simple unit conversions to more complex, multi-step calculations involving several different quantities. Work the following exercises!! Measurements are made using a variety of units. Wouldn't m/s *s/1 = ms/s? Dimensional analysis provides us with the tools needed to convert between different units of measure. The space between the two temperatures is divided into 100 equal intervals, which we call degrees. 18- Oh, it's 18,000, 18,000, 18,000 meters. formula or an equation, which could be really, really helpful to make sure that we're There are many ways to solve these problems which will depend on what equivalences you remember. A Toyota Prius Hybrid uses 59.7 L gasoline to drive from San Francisco to Seattle, a distance of 1300 km (two significant digits). Using unit conversion / dimensional analysis to calculate the volume of the solution in mL. Dimension conversions of Y into inches. Where applicable, start with a British unit and convert to metric, vice versa, etc. 1. seconds in the denominator multiplied by seconds in the numerator. Unit analysis is a form of proportional reasoning where a given measurement can be multiplied by a . - A milliliter (mL) is a cube 1 centimeter (cm) long on each side, also called 1 cubic centimeter (cm cm cm = cm 3 ). water to liters of water. What is this temperature on the kelvin scale and on the Fahrenheit scale? (b) Using the previously calculated volume in gallons, we find: \[\mathrm{56.3\: gal\times\dfrac{$3.80}{1\: gal}=$214} \nonumber \]. Type in your own numbers in the form to convert the units! Let's do another example of a unit conversion. In the first step, we have to cancel out "an ounce of Mg", so we plug in the known value for the number of grams in an ounce (28.35). Dimensional analysis is based on this premise: the units of quantities must be subjected to the same mathematical operations as their associated numbers. The best way to ensure an accurate conversion is to use a scale. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. The Stoichiometry of Product Formation and Percent Yield, Determining the Empirical Formula of a Compound from its Molecular Formula, Determining the Empirical Formula from an Elemental Analysis, (from a complete OLI stoichiometry course). Express your answer to the correct number of significant figures. 1000 grams over 1 kilogram is equal to 1. (When identical units divide to yield a factor of 1, they are said to cancel.) Using dimensional analysis, we can determine that a unit conversion factor has been set up correctly by checking to confirm that the original unit will cancel, and the result will contain the sought (converted) unit. 5. multiple times in our life that distance can be }\right)\times length\: in\: inches} \nonumber \]. If gasoline costs $3.80 per gallon, what was the fuel cost for this trip? Example \(\PageIndex{3}\): Computing Quantities from Measurement Results. Convert 1.500 days into minutes and seconds. chemical quantities, it is important to remember that each quantity is associated with both a unit and a chemical &=\mathrm{4.41\: oz\: (three\: significant\: figures)} Metric Units and Dimensional Analysis. Convert 1.64 pounds to grams and milligrams. \[\mathrm{4.00\:\cancel{qt}\times\dfrac{1\: L}{1.0567\:\cancel{qt}}=3.78\: L}\nonumber \], \[\mathrm{3.78\:\cancel{L}\times\dfrac{1000\: mL}{1\:\cancel{L}}=3.78\times10^3\:mL}\nonumber \], \[\mathrm{density=\dfrac{4.20\times10^3\:g}{3.78\times10^3\:mL}=1.11\: g/mL}\nonumber \]. 6.74 x 10 27 molecules H 2. Hang around your classroom or put in classroom table buckets.This packet includes:- 12 long strips of basic conversions- 3 whole sheets of basic conversions (meters, liters, and grams)- 1 reference sheet for perimeter, area, and volume formulas**This pro. \times \dfrac{2.54\: cm}{1\:\cancel{in. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. Using this equivalence we have: Sometimes, you might have to use 3, 4, 5 or more equivalences to get the desired unit. The conversion between the two units is based on the fact that 1 liter is defined to be the volume of a cube that has sides of length 1 decimeter. When we multiply a quantity (such as distance given in inches) by an appropriate unit conversion factor, we convert the quantity to an equivalent value with different units (such as distance in centimeters). 454 grams = 1 lb, 1 qt = 1.09 liters, 2.54 cm = 1 inch). The International System of Units (SI) specifies a set of seven base units from which all other units of measurement are formed. Volume in ml = Volume in cm 3. For example, the lengths of 2.54 cm and 1 in. CoolGyan'S online dimensional 24/7 support Our team is available 24/7 to help you with whatever you need. 0.23 mol oxygen, or 3.0 x 1021 atoms sodium. Have feedback to give about this text? To convert from dimes to dollars, the given (20 dimes) is multiplied by the conversion factor that cancels out the unit dimes. Required fields are marked *. Although there is a way to develop a conversion factor which will give us a one-step calculation, for the sake of this example, lets proceed with a two-step method. Having identified the units and determined the conversion factor, the calculation is set up as follows: Notice that the conversion factor used has the given units in the denominator which allows for proper cancellation of the units, that is, the given units cancel out, leaving only the desired units which will be in the answer. 1 liter per 100 centiliters. them. So, both 3s go away, and you're left with 2 divided by 1, or simply 2. We've now expressed our distance in terms of units that we recognize. One way we measure a change in temperature is to use the fact that most substances expand when their temperature increases and contract when their temperature decreases. and are left with grams water. \(T_\mathrm{^\circ C}=\dfrac{5}{9}\times T_\mathrm{^\circ F}-32\), \(T_\mathrm{^\circ F}=\dfrac{9}{5}\times T_\mathrm{^\circ C}+32\). Direct link to Kim Seidel's post Yes, "m/s *s/1 = ms/s". Conversion Factors Part 3: Multi-Step 2 videos the answer in meters but we wanted the answer in kilometers? But, if you're tired of getting your conversions wrong, this blog post has got you covered. more complicated example. 1 liters to grams = 1000 grams. If starting with grams, we use 1 mL/19.3g to . Stoichiometry Tutorials: Dimensional Analysis / Stoichiometric Conversions. In problem solving, proper care in setting up calculations is very important, and special attention should always be given to unit cancellation. \[\mathrm{^\circ C=\dfrac{5}{9}(^\circ F-32)=\dfrac{5}{9}(450-32)=\dfrac{5}{9}\times 418=232 ^\circ C\rightarrow set\: oven\: to\: 230 ^\circ C}\hspace{20px}\textrm{(two significant figures)}\nonumber \], \[\mathrm{K={^\circ C}+273.15=230+273=503\: K\rightarrow 5.0\times 10^2\,K\hspace{20px}(two\: significant\: figures)}\nonumber \]. Example \(\PageIndex{2}\): Computing Quantities from Measurement Results. gold's density is 19.3 grams per mL. Glassware for Measuring Volume We begin by writing down our initial quantity of 4.1 kilograms water. Listed below are some other common unit conversions as well as common metric prefixes used in science. Describe how to use dimensional analysis to carry out unit conversions for a given property and computations involving two or more properties. Direct link to Nichole's post There's not much differen, Posted 7 years ago. View Answer. Dimensional analysis is a way chemists and other scientists convert unit of measurement. a) If the density of the fuel is 0.768 g/cm3, what is the mass of the fuel in kilograms? Show the expression setup and cancel units in the whiteboard area, below. The units worked out. actually be quite useful, and this thing that I'm can really be viewed as algebraic objects, that you can treat them like variables as we work through a One application of rational expressions deals with converting units. Spring 2015 REEL Chemistry Student Presentations, REEL Chemisry Student Presentations Spring 2014, 2016 Annual Chemistry Teaching Symposium and Education Exhibition, Worksheet: Conversion Factors and Roadmaps, Conversion Factors Part 3: Multi-Step 2 videos, Back to Study Guide List for General Chemistry I, 8. Back to Study Guide List for General Chemistry I What's neat here is we Following the same approach, the equations for converting between the kelvin and Celsius temperature scales are derived to be: \[T_{\ce K}=T_{\mathrm{^\circ C}}+273.15 \nonumber \], \[T_\mathrm{^\circ C}=T_{\ce K}-273.15 \nonumber \]. The correct unit conversion factor is the ratio that cancels the units of grams and leaves ounces. The freezing temperature of water on this scale is 273.15 K and its boiling temperature 373.15 K. Notice the numerical difference in these two reference temperatures is 100, the same as for the Celsius scale, and so the linear relation between these two temperature scales will exhibit a slope of \(\mathrm{1\:\dfrac{K}{^\circ\:C}}\). Once again, dimensional analysis has helped us express a When a scale is not available, a calculator like the one above is a good way to estimate the volume to weight conversion. Solute, Solvent, Solution Relationship 5. For example, we will write 4.1 kg water, or If you convert it back to the original unit, the number should be the same. In the practice, many of the problems have the problems expressed in meters squared or cubed, but the video does not explain how to handle the numbers when converting from say, cm3 to m3 (sorry I don't know how to subscript!) water. We're going to get distance is Our goal is to convert the units of the denominator from milliliters of Example \(\PageIndex{4}\): Computing Quantities from Measurement Results. First, we need an equivalence. As complex as some chemical calculations seem, the dimensional analysis involved remains as simple as the preceding exercise. Normal body temperature has been commonly accepted as 37.0 C (although it varies depending on time of day and method of measurement, as well as among individuals). The 273.15 in these equations has been determined experimentally, so it is not exact. While it is true that 12 inches equals 1 foot, you have to remember that 12 in 3 DOES NOT equal 1 . 1 teragram/liter [Tg/L] = 1000000000000 kilogram/cubic meter. To solve it you need to know that, as always, there are 6.02 x 10 23 molecules (or atoms) of whatever in a mole. teragram . On the Fahrenheit scale, the freezing point of water is defined as 32 F and the boiling temperature as 212 F. The multiplication gives the value of and then convert volume from liters to gallons: \[\mathrm{213\:\cancel{L}\times\dfrac{1.0567\:\cancel{qt}}{1\:\cancel{L}}\times\dfrac{1\: gal}{4\:\cancel{qt}}=56.3\: gal} \nonumber\], \[\mathrm{(average)\: mileage=\dfrac{777\: mi}{56.3\: gal}=13.8\: miles/gallon=13.8\: mpg} \nonumber\]. If the units cancel properly, the problem should solve correctly. If gasoline costs $3.90 per gallon, what was the fuel cost for this trip? 0.01 m 3 / 0.001 [ (m 3) / (L) ] = 10 L. To convert among any units in the left column, say from A to B, you can multiply by the factor for A to convert A into m/s 2 then divide by the factor for B to convert out of m 3 . Just print, laminate, cut, hole punch, and add to a ring. For example, if your equation involves the use of the 60min/hour conversion factor, you can multiply by it (60min/hr) or divide by it (hr/60 min), but you can' t move . Then, the fraction you wrote in Step 3 that allows you to cancel out the unit you started with (cm), and multiply. Recall that we do not use the degree sign with temperatures on the kelvin scale. Beyond simple unit conversions, the factor-label method can be used to solve more complex problems involving computations. The basis for this method is keeping track of the units of the components in the calculations. Now, consider using this same relation to predict the time required for a person running at this speed to travel a distance of 25 m. The same relation between the three properties is used, but in this case, the two quantities provided are a speed (10 m/s) and a distance (25 m). These conversions are accomplished using unit conversion factors, which are derived by simple applications of a mathematical approach called the factor-label method or dimensional analysis. Because the numerators equal the denominators, the conversion factors = 1, so . 100 grams to liter = 0.1 liter. When we multiply a quantity (such as distance given in inches) by an appropriate unit conversion factor, we convert the quantity to an equivalent value with different units (such as distance in centimeters). We'd want to multiply this thing by something that has It is often useful or necessary to convert a measured quantity from one unit into another. Baking a ready-made pizza calls for an oven temperature of 450 F. . A particularly useful unit in chemistry is that of the mole. To answer this question, you will need to recall one fact of converting between customary and metric systems: 1 inch = 2.54 cm. To convert from kilograms to grams, use the relationship 1kg=1000g. someone gave us the time. We can state the following two relationships: This is the first part of the road map. PDF. viewed as rate times time. In our example, we are asked how many dollars equal 20 dimes. For instance, it allows us to convert between volume expressed in liters and volume expressed in gallons. between volume expressed in liters and volume expressed in gallons. A: Click to see the answer. grams of water per 1 kilogram water. Third, convert ml to L. 1 L = 1000 ml. Example: Use dimensional analysis to find the missing quantity. xoz = 125 g 1oz 28.349 g = ( 125 28.349)oz = 4.41oz(threesignificantfigures) Exercise 1.2.1. . We write the unit conversion factor in its two forms: \[\mathrm{\dfrac{1\: oz}{28.349\: g}\:and\:\dfrac{28.349\: g}{1\: oz}} \nonumber\]. The highest temperature recorded in . and then convert volume from liters to gallons: \[\mathrm{213\:\cancel{L}\times\dfrac{1.0567\:\cancel{qt}}{1\:\cancel{L}}\times\dfrac{1\: gal}{4\:\cancel{qt}}=56.3\: gal}\nonumber \], \[\mathrm{(average)\: mileage=\dfrac{777\: mi}{56.3\: gal}=13.8\: miles/gallon=13.8\: mpg}\nonumber \]. This strategy is also employed to calculate sought quantities using measured quantities and appropriate mathematical relations. This is why it is referred to as the factor-label method. What I want to do in this video is use this fairly simple A 4.00-qt sample of the antifreeze weighs 9.26 lb. Consider, for example, the quantity 4.1 kilograms of water. Would this work using any formula, like a=F/m? density=0.124kg1893mm3. Step 4: Write down the number you started with in the problem (55 cm). Divide the mass by the volume in order to find the density, and then use conversion factors to cancel the given units and leave the desired units. A conversion between the two units could be performed using dimensional analysis. You must remember to "distribute" the cube. Click here. We can write two conversion factors for each equivalence.