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Our goal is to convert the units of the denominator from milliliters of Most measurement units for a given property are directly proportional to one another (y = mx). Direct link to elise's post In the practice, many of , Posted 4 years ago. Dimensional analysis is the process of converting between units. b) If the jet weights 443.613 Mg without passengers or fuel, what is the mass when the fuel is added? The correct unit conversion factor is the ratio that cancels the units of grams and leaves ounces. In this section, you will look at common unit conversions used in science. Next we multiply by the ratio 1000 18,000 divided by 1,000 is equal to 18. \u0026 Dimensional Analysis General Physics - Conversion of Units Examples Shortcut for Metric Unit Conversion PLTW IED - Unit Conversion 3.2 Notes . 1 L = 10-6 L. Notice that one equivalence and one set of conversion factors is written for each arrow in the roadmap. To answer this question, you will need to recall one fact of converting between customary and metric systems: 1 inch = 2.54 cm. A sample of calcium nitrate, Ca (NO3)2, with a formula weight of 164 g/mol, has 5.00 x 1025 atoms of oxygen. But let's just use our little dimensional analysis muscles a little bit more. To determine how many gallons in 24 quarts we first need to set up an equivalence. and then convert volume from liters to gallons: \[\mathrm{213\:\cancel{L}\times\dfrac{1.0567\:\cancel{qt}}{1\:\cancel{L}}\times\dfrac{1\: gal}{4\:\cancel{qt}}=56.3\: gal}\nonumber \], \[\mathrm{(average)\: mileage=\dfrac{777\: mi}{56.3\: gal}=13.8\: miles/gallon=13.8\: mpg}\nonumber \]. dimensional analysis. A commercial jet is fueled with 156,874 L of jet fuel. Given 500.0 Liters of H 2 gas, convert to molecules. For example, if someone What if it doesn't say how many seconds like, "Uche pumps gasoline at a rate of 18 .". The number of conversion factors used for each problem will depend on the types and number of equivalences that you use. the proportionality constant, m, is the conversion factor. The 273.15 in these equations has been determined experimentally, so it is not exact. Step 3: Finally, the dimensional analysis will be displayed in the new window. Hope this helped! Download File PDF Ied 32a Unit Conversion Answers (Meters, Liters, Grams, \u0026 more) - [5-8-1] How to Convert Unit metre to cm Meter to ft . Dimension Y = 250cm. The correct unit conversion factor is the ratio that cancels the units of grams and leaves ounces. 1. There are many ways to solve these problems which will depend on what equivalences you remember. Since 1 L equals dm 3, I have my volume in liters. [4] Physical quantities that are commensurable have the same dimension; if they have different dimensions, they are incommensurable. We can take this definition and form ratios: These ratios are useful, since they allow us to convert from quantities in grams to quantities in kilograms and 8 cups in grams converter to convert 8 cups to grams and vice versa. The volume of a sphere is 4 3r3. Quick conversion chart of grams to liter. We have been using conversion factors throughout most of our lives without realizing it. Q: An equilibrium is established for the exothermic reaction Br (g) + 5 F (g) = 2 BrF, (g). You can use this simple formula to convert: Thus, the volume in grams is equal to the liters multiplied by 1,000 times the density of the ingredient or material. In order to use dimensional analysis, we must first talk about conversion factors. 10 grams to liter = 0.01 liter. For this, you need to know the molar mass of methane, which is 16.04 g/mol. It's useful for something as simple as distance equals rate times time, but as you go into physics milliliter of water, and we want to express this in units of grams of water per liter of water. }\:(2.54\: cm=1\: in. 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. that we're familiar with. 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, \[\mathrm{\dfrac{100\: m}{10\: s}=10\: m/s} \nonumber \]. 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). Posted 5 years ago. The equivalence is written as. This is the conversion factor we can use to convert betweeen these two measurements of weight. Just as for numbers, a ratio of identical units is also numerically equal to one. Why does this say d= rate x time so if I take the birth rate in the US and multiply it by a time, I will get a distance? water to liters of water. One gallon is 3.79 liters (1 gal = 3.79 liters). It is important to identify the given and the desired quantities in any problem. In working with To mark a scale on a thermometer, we need a set of reference values: Two of the most commonly used are the freezing and boiling temperatures of water at a specified atmospheric pressure. Dimensional analysis is based on this premise: the units of quantities must be subjected to the same mathematical operations as their associated numbers. }=1} \nonumber \]. between volume expressed in liters and volume expressed in gallons. Remember that 1000 g and 1 kg are the same thing, so we are just multiplying Jan 15, 2015. Dimensional analysis is based on this premise: the units of quantities must be subjected to the same mathematical operations as their associated numbers. It will take seconds for the device to release 154 grams of the gas. What is this temperature on the kelvin scale and on the Fahrenheit scale? (1 gram = 15.432 grains) Solve using the conversion factors that are listed in the table below. 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. But what's neat is when you multiply, we have meters canceling with meters, and so you're left with 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 need to use two steps to convert volume from quarts to milliliters. Unit analysis is a form of proportional reasoning where a given measurement can be multiplied by a . We will provide six simple tricks that make converting gallons, quarts and fluid ounces easier than ever beforeso no more guessing or using outdated estimations. 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. Meave60. The necessary conversion factors are given in Table 1.7.1: 1 lb = 453.59 g; 1 L = 1.0567 qt; 1 L = 1,000 mL. How many milliliters of ethyl alcohol will he measure? This will help you keep track Direct link to Nichole's post There's not much differen, Posted 7 years ago. 18- Oh, it's 18,000, 18,000, 18,000 meters. Say we are given the density of water as one gram of water per Now that you have volume in L and density in kg/L, you simply multiply these together to get the mass of the substance of interest. This metric system review video tutorial provides an overview / review of how to convert from one unit to another using a technique called dimensional analysis or the factor label method. For instance, it allows us to convert between volume expressed in liters and volume expressed in gallons. 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. For example, a dime isnt the same amount as a dollar, but ten dimes equals the same amount of money as one dollar. The gram, or gramme, is an SI unit of weight in the metric system. Are there any videos doing this type of rate conversion? Most of us could have performed the calculation without setting up equivalences and conversion factors. I don't think this happens often, but if you think about it, 18 is the same thing as 18/1, so it's basically saying that Uche pumps 18 gallons every second. 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 . We write the unit conversion factor in its two forms: \[\mathrm{\dfrac{1\: oz}{28.349\: g}\:and\:\dfrac{28.349\: g}{1\: oz}}\nonumber \]. Alternatively, the calculation could be set up in a way that uses three unit conversion factors sequentially as follows: \[\mathrm{\dfrac{9.26\:\cancel{lb}}{4.00\:\cancel{qt}}\times\dfrac{453.59\: g}{1\:\cancel{lb}}\times\dfrac{1.0567\:\cancel{qt}}{1\:\cancel{L}}\times\dfrac{1\:\cancel{L}}{1000\: mL}=1.11\: g/mL} \nonumber\]. Using the above conversion factors, make the following conversions. The mole is defined as Avogadro's number of items, PDF. What is the density of common antifreeze in units of g/mL? 1 mole over Avogadro's number of items equals 1, Avogadro's number of items over 1 mole equals 1. Keep in mind that each type of problem can be done with as many or as few conversion factors as you can write. Measurements are made using a variety of units. Now, you know that in 105 g of methane there are 6.55 mol of methane. The calculation of density is quite straightforward. Next, you can make use of Avogadro's number to find the . Describe how to use dimensional analysis to carry out unit conversions for a given property and computations involving two or more properties. Thus, the volume in grams is equal to the liters multiplied by 1,000 times the density of the ingredient or material. (1) $5.00. 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. To use this you need to identify conversion factors. We begin by writing down our initial quantity of 4.1 kilograms water. 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. (a) We first convert distance from kilometers to miles: \[\mathrm{1250\: km\times\dfrac{0.62137\: mi}{1\: km}=777\: mi}\nonumber \]. Instead of giving it in Judged on the practice, there feels like there is more to it than this. As mentioned earlier in this chapter, the SI unit of temperature is the kelvin (K). Consider, for example, the quantity 4.1 kilograms of water. itself. $$5700cm^{3}*\left ( \frac{1in}{2.54cm} \right )^{3}=347.6in^{3}$$. A conversion between the two units could be performed using dimensional analysis. A ratio of two equivalent quantities expressed with different measurement units can be used as a unit conversion factor. &=\mathrm{\left(\dfrac{125}{28.349}\right)\:oz}\\ [1] The density of dry ingredients can vary for a variety of reasons, such as compaction. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. $$5700cm^{3}*\frac{1in^{^{3}}}{16.4cm^{3}}=347.6cm^{3}$$. Dimensional analysis allows us to convert units between different scales. We're done. viewed as rate times time. For now we want to concentrate on setting up conversion factors, but as a preview to dimensional analysis, the following calculation shows how the conversion factor is used. To simply convert from any unit into kg/m 3, for example, from 50 lb/ft 3, just multiply by the value in the right column in the table below. 2. Convert the pressures recorded in hPa into atm through dimensional analysis. Example \(\PageIndex{1}\): Using a Unit Conversion Factor. 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.. xoz = 125 g 1oz 28.349 g = ( 125 28.349)oz = 4.41oz(threesignificantfigures) Exercise 1.2.1. What is the volume in liters of 1.000 oz, given that 1 L = 1.0567 qt and 1 qt = 32 oz (exactly)? Because the numerators equal the denominators, the conversion factors = 1, so . The equations technically look the same, but you're going to get a goofy answer if your distance unit is babies*time. Conversion Factors Part 3: Multi-Step 2 videos 2 Jul. Convert 250 Mg ->g Using Dimensional Analysis. 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. gives us the ratios. Found a typo and want extra credit? A ratio of two equivalent quantities expressed with different measurement units can be used as a unit conversion factor. If you want to get the most useful . 1.6 Unit Conversion Word Problems. There is nothing much to worry We know distance = Speed * Time, I don't understand why m/s * s cancels out the two s's? One application of rational expressions deals with converting units. 1. In any problem or calculation involving conversions, we need to know the units involved, in this case the units are dimes and dollars. Type in your own numbers in the form to convert the units! We write the unit conversion factor in its two forms: \[\mathrm{\dfrac{1\: oz}{28.349\: g}\:and\:\dfrac{28.349\: g}{1\: oz}} \nonumber\]. Hope this helps! 2) The conversions: first ---> convert cubic feet to cubic inches second ---> convert in 3 to cubic centimeters third ---> convert cm 3 to mL fourth ---> convert mL to L. 3) Comment: Note the (12 inch) 3. It provides unit conversion practice problems that relates to chemistry, physics, and algebra. Figure \(\PageIndex{1}\) shows the relationship among the three temperature scales. 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. The basis for this method is keeping track of the units of the components in the calculations. Using this equivalence we have: Sometimes, you might have to use 3, 4, 5 or more equivalences to get the desired unit. (This is a very common conversion.) hours in the denominator and seconds in the numerator, times essentially seconds per hour. 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 A: Answer:- This question is answered by using the simple concept of calculation of pH during the. substance, and it is important to always write both of these down. Liters and grams are both commonly used to measure cooking ingredients. The content above has been converted from Adobe Flash Player and may not display correctly. Use Dimensional Analysis. 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 generally used to categorize types of physical quantities and units based on their relationship to or dependence on other units.\"Wikipedia contributors. What (average) fuel economy, in miles per gallon, did the Prius get during this trip? 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. If the units cancel properly, the problem should solve correctly. Representing the Celsius temperature as \(x\) and the Fahrenheit temperature as \(y\), the slope, \(m\), is computed to be: \[\begin{align*} m &=\dfrac{\Delta y}{\Delta x} \\[4pt] &= \mathrm{\dfrac{212\: ^\circ F - 32\: ^\circ F}{100\: ^\circ C-0\: ^\circ C}} \\[4pt] &= \mathrm{\dfrac{180\: ^\circ F}{100\: ^\circ C}} \\[4pt] &= \mathrm{\dfrac{9\: ^\circ F}{5\: ^\circ C} }\end{align*} \nonumber \]. You may do simple problems like this frequently throughout the day. 500 grams to liter = 0.5 liter. 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 (\(b\)). Direct link to Kim Seidel's post Yes, "m/s *s/1 = ms/s". A 4.00-qt sample of the antifreeze weighs 9.26 lb. 1 grams to liter = 0.001 liter. Recall that we do not use the degree sign with temperatures on the kelvin scale. were to give you a rate, if they were to say a rate of, let's say, 5 meters per second, and they were to give you a time, a time of 10 seconds, then we can pretty, in a Next, you need to determine the conversion factors from this equality. We can convert mass from pounds to grams in one step: \[\mathrm{9.26\:\cancel{lb}\times \dfrac{453.59\: g}{1\:\cancel{lb}}=4.20\times 10^3\:g}\nonumber \]. Convert 7.2 meters to centimeters and inches. 1 L 1000 ml. 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). Figure 2.3. }\right)\times length\: in\: inches} \nonumber \]. Those are going to cancel out, and 5 times 10, of course, is, 5 times 10, of course, is 50. He is doing that to get rid of "hour", and to replace it with "seconds". Identify the given units and the desired units: If its not a single step calculation, develop a road map. Quick conversion chart of liters to grams. Example: Use dimensional analysis to find the missing quantity. Dimensional analysis provides us with the tools needed to convert between different units of measure. The numbers of these two quantities are multiplied to yield the number of the product quantity, 86, whereas the units are multiplied to yield. \nonumber \]. For example, 1 liter can be written as 1 l, 1 L, or 1 . Your cruise ship is leaving for a 610-league adventure. The highest temperature recorded in . Back to Study Guide List for General Chemistry I 5 l = 5 1,000 0.7 = 3,500 g. We need to figure out the number of grams in 3 liters of water. \[x\:\mathrm{oz=125\: g\times unit\: conversion\: factor} \nonumber\]. In the meantime, you will need to practice, practice, and more practice. pretty straightforward way, apply this formula. 1: One centimeter cubed is the volume occupied by a cube with an edge length of 1 cm . By making "hours" the denominator, the "hours" will cancel out since (hour)/(hour) is 1, and then the only time unit left is "seconds". There are 1000 cm 3 in 1 dm 3. Show the expression setup and cancel units in the whiteboard area, below. 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. Volume in ml = 15625 ml. Learn what is dimensional analysis and go through various dimensional analysis examples to master the content by reading this article! To convert this to molecules of water, we multiply by the 5.0. Using these two pieces of information, we can set up a dimensional analysis conversion. multiple times in our life that distance can be The trick with this way of doing the calculation is you have to remember to apply the power to EVERYTHING: $$\left ( \frac{1in}{2.54cm} \right )^{3}=\frac{\left ( 1^{3}in^{3} \right )}{2.54^{3}cm^{3}}$$. You can learn anything! If we have the conversion factor, we can determine the mass in kilograms using an equation similar the one used for converting length from inches to centimeters. our end units for distance were in meters, which For now we will focus on single step conversions. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Please provide any two values to the fields below to calculate the third value in the density equation of. With square units, you would need to square the conversion factor. Note: We are ignoring a concept known as "significant figures" in this example. definition, we know this ratio is equal to 1, so we are changing only the unit of the quantity, not the quantity The procedure to use the Dimensional Analysis calculator is as follows: Step 1: Enter two physical quantities in the respective input field. You must remember to "distribute" the cube. Grams, g Milligram, mg Micrograms, ug: 1 kg = 1000 g= 10 3 g 1 . )\: or\: 2.54\:\dfrac{cm}{in.}}\]. have successfully converted the density of water from units of grams per milliliter to units of grams per liter. It is great because is shows the relationship between the units. Voiceover:We've seen For this Converting from one dimensional unit to another is often somewhat complex. 1 amu = 1.6606 x 10 -24 grams. 1 lb = 0.45 kg Work the following exercises!! To yield the sought property, time, the equation must be rearranged appropriately: \[\mathrm{time=\dfrac{distance}{speed}} \nonumber \], \[\mathrm{\dfrac{25\: m}{10\: m/s}=2.5\: s} \nonumber \], 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.. 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. Dimensional analysis is used in science quite often. Converting units does not change the actual value of the unit. In 1848, British physicist William Thompson, who later adopted the title of Lord Kelvin, proposed an absolute temperature scale based on this concept (further treatment of this topic is provided in this texts chapter on gases). Online calculator: Convert grams to liters and liters to grams Example: Water density is 1000 kg/m3. Joe is the creator of Inch Calculator and has over 20 years of experience in engineering and construction. 1 kilogram over 1000 grams is equal to 1. Just print, laminate, cut, hole punch, and add to a ring. A: Click to see the answer. (5) What is the density of mercury (13.6 g/cm 3) in units of kg/m 3 . The space between the two temperatures is divided into 100 equal intervals, which we call degrees. I don't t. I'll do it in this color. Direct link to Neil Gabrielson's post Great question! Many chemistry problems require unit conversions and this is a good method to use regardless of the type of problem encountered. What is the kelvin temperature? View Answer. A 4.00-qt sample of the antifreeze weighs 9.26 lb. 1 L 4.22675 US cups = 4.22675 US cups 1 L = 1. For example, consider measuring the average speed of an athlete running sprints. - A liter is a cube 1 decimeter (dm) long on each side. \[x\:\mathrm{oz=125\: g\times unit\: conversion\: factor}\nonumber \]. Regardless of the details, the basic approach is the sameall the factors involved in the calculation must be appropriately oriented to insure that their labels (units) will appropriately cancel and/or combine to yield the desired unit in the result. One of the conversion factors will be used for the calculation. Say we want to convert this quantity to grams of The multiplication gives a value of one thousand and units of grams of water per liter of water, so we . left with are the meters, 50 meters. An oxygen atom has a diameter of 1.2 x 10-10 m. What is the volume, in liters, of 6.46 x 1024 oxygen atoms? The actual weight of a liter will vary depending on the density of the material. A liter is sometimes also referred to as a litre. Several other commonly used conversion factors are given in Table \(\PageIndex{1}\). What is the volume in liters of 1.000 oz, given that 1 L = 1.0567 qt and 1 qt = 32 oz (exactly)? While being driven from Philadelphia to Atlanta, a distance of about 1250 km, a 2014 Lamborghini Aventador Roadster uses 213 L gasoline. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. formula right over here, this fairly simple equation, to understand that units Step 2: Now click the button "Submit" to get the analysis. This method is called dimensional analysis and will be an important part of problem solving in any science course. 1. 1. Here's a chemistry problem. We know we're going to use moles eventually (because a chemical equation is involved), so we look at the Periodic table and find that 1 mole of Mg weighs 24.31 . This page titled E.4: Unit Conversion & Dimensional Analysis is shared under a CC BY license and was authored, remixed, and/or curated by OpenStax. First, set up a conversion factor. x\:\ce{oz}&=\mathrm{125\:\cancel{g}\times \dfrac{1\: oz}{28.349\:\cancel{g}}}\\ That's 5 times 3,000 would be 15,000, 5 times 600 is another 3,000, so that is equal to 18,000. Use this page to learn how to convert between liters and grams. ratio "Avogadro's number of water molecules per mole of water molecules". 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). This method can be applied to computations ranging from simple unit conversions to more complex, multi-step calculations involving several different quantities. The 5 times the 1, so we multiply the 5 times the 1, that's just going to give us 5. Dimensional Analysis is a powerful way to solve problems. 4. Alternatively, the calculation could be set up in a way that uses all the conversion factors sequentially, as follows: \[\mathrm{\dfrac{1250\:\cancel{km}}{213\:\cancel{L}}\times\dfrac{0.62137\: mi}{1\:\cancel{km}}\times\dfrac{1\:\cancel{L}}{1.0567\:\cancel{qt}}\times\dfrac{4\:\cancel{qt}}{1\: gal}=13.8\: mpg}\nonumber \]. The necessary conversion factors are given in Table 1.7.1: 1 lb = 453.59 g; 1 L = 1.0567 qt; 1 L = 1,000 mL. $$5.70 L*\frac{1000 mL}{1 L}*\frac{1 cm^{3}}{1 mL}=5700cm^{3}$$. Example \(\PageIndex{3}\): Computing Quantities from Measurement Results. Convert 50.0 mL to liters. Online Resources for Teaching and Learning Chemistry, See home page (click here) for information on coronovirus (Covid-19), Dimensional Analysis/Stoichiometric Conversions, Dimensional analysis allows us to change the units used to express a value. Next, we need to setup the calculation. Step 4: Write down the number you started with in the problem (55 cm). First, we need an equivalence. Well, we could take that 18,000 meters, 18,000 meters, and if we could multiply it by something that has meters in the denominator, meters in the denominator and kilometers in the numerator, then these meters would cancel out, and we'd be left with the kilometers. 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. If gasoline costs $3.80 per gallon, what was the fuel cost for this trip? rate at 5 meters per second, but let's say that To convert from kg/m 3 into units in the left column divide by the value in the right column or, multiply by the reciprocal, 1/x. (a) We first convert distance from kilometers to miles: \[\mathrm{1250\: km\times\dfrac{0.62137\: mi}{1\: km}=777\: mi} \nonumber\]. If you have a question, please ask in the comment section. I know this is a really dumb question, but I just need a clarification I guess. Here is a video with some more challenging examples: enter link . muscles a little bit more. \times \dfrac{2.54\: cm}{1\:\cancel{in. Web. This doesn't feel like our Volume in ml = Volume in cm 3. Since \(\mathrm{density=\dfrac{mass}{volume}}\), we need to divide the mass in grams by the volume in milliliters.