What is Ratio: Definition and 1000 Discussions

In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8∶6, which is equivalent to the ratio 4∶3). Similarly, the ratio of lemons to oranges is 6∶8 (or 3∶4) and the ratio of oranges to the total amount of fruit is 8∶14 (or 4∶7).
The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be positive.
A ratio may be specified either by giving both constituting numbers, written as "a to b" or "a∶b", or by giving just the value of their quotient a/b. Equal quotients correspond to equal ratios.
Consequently, a ratio may be considered as an ordered pair of numbers, a fraction with the first number in the numerator and the second in the denominator, or as the value denoted by this fraction. Ratios of counts, given by (non-zero) natural numbers, are rational numbers, and may sometimes be natural numbers. When two quantities are measured with the same unit, as is often the case, their ratio is a dimensionless number. A quotient of two quantities that are measured with different units is called a rate.

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  1. P

    Ratio of RMS Speed of Oxygen to Nitrogen Molecules

    Homework Statement A container is filled with a mixture of nitrogen and oxygen. What is the ratio of the rms speed of oxygen molecules to that of nitrogen molecules? (Molar mass of oxygen=32gmol-1; molar mass of nitrogen=28gmol-1). Homework Equations v2=(v12+v22+...+vN2)/N The...
  2. G

    Ratio of µ in a rope with differing thickness/Waves

    Homework Statement For the cord in the following diagram, what is the ratio of µ for the different sections to create a Γ/2 on the right? *** The picture depicts a rope with an upward oriented reflected pulse on the left (thinner rope) and a downward oriented transmitted pulse on the right...
  3. D

    Ratio test for convergence of series 1/log(n)?

    Hi. I have been banging my head against this problem for a while and I just don't get it. Maybe (probably) it's something wrong with my logarithm-fu or limit-fu. I just registered to ask this because I couldn't find an answer anywhere, and I've been reading these forums for a while for other...
  4. H

    Glashow model left/right hypercharge ratio

    Homework Statement a) Consider Glashow's model with general hypercharge assignments Y_L, Y_R, for the left-handed and right-handed fields, respectively. By demanding the correct electromagnetic couplings of the electron and neutrino to the photon, determine the ratio Y_L/Y_R. [8 marks]...
  5. M

    Experiment: Ratio of the principal specific heat capacities of air

    Homework Statement To find the ratio of the specific heat capacities of air (γ). Homework Equations PVγ=constant The Attempt at a Solution I performed the experiment a number of times to get an average for γ The experiment consisted of a container with release valve, a hand...
  6. E

    Ratio of Pressures Involving Piston Strokes

    Homework Statement If the cross-section of the barrel of a pump is 5 square centimeters, the stroke of the piston is 20 centimeters, and the volume of the receiver, in which the air is drawn from, is 1 liter, calculate the ratio of the pressure of the air in the receiver to the original...
  7. A

    What is the difference between compression ratio and cut off ratio?

    I know the cut off ratio is of the specific volumes, but is that it? And what exactly do they tell you
  8. wolram

    What is the Gender Ratio of Online Users?

    Its not obvious to tell by handles, so what is the ratio of female to male users.
  9. A

    Calculating car tyre forces - slip ratio

    In most tyre models we look at the slip ratio between the tyre and the road to help determine the amount of force that the tyre can generate. My question is, why is it the ratio that is so important? If a vehicle is doing 100m/s and the tyre is at 90m/s then the relative velocity against the...
  10. R

    Velocity ratio of a third class lever

    Homework Statement 3rd class lever 5m distance from load to effort and 1m distance from effort to pivot. Load = 1962 Effort required to lift load = 11772N MA = 0.16 or 1/6 ( so there really is no MA) Calculate the velocity ratio of the system ? Homework Equations I have...
  11. D

    Signal-Noise Ratio: Decibels & Resolving Signals

    I am trying to get an understanding of what a good signal to noise ratio in terms of decibels. My SNR is roughly 20 dB, and am concerned about being able to resolve the signal from this.
  12. I

    Ratio of number density of photons to baryons

    Homework Statement photon/baryon ratio = Np/Nb Np, is the number density of the CMB photons Nb, is the number density of baryons Evaluate this ratio at the redshifts z=0 and z=100. From my understanding, if interactions are negligable, particles cannot simply disappear. Therefore...
  13. Q

    Nucleus stability: Neutron & Proton Ratio

    Hi I'm looking for a good description (high-school to 1st year level) why the ratio of protons to neutrons matters for stability. Single neutrons are unstable, but in a nucleus they are stable and the more nucleons you have the greater the strong force. So why can't you have stable isotopes...
  14. G

    Floating Wood: Finding the Ratio Above Water

    A block of wood with a density that is 750 kg/m3 is floating in a tank of water. How much of the wood is above the surface of the water D=M/V I've been trying for hours to try to figure this one out. The only info I'm given the the density of a block of wood in the water at...
  15. B

    Modeling Turbo RPM for Desired Pressure Ratio in BMW

    I am trying to model the RPM at which the turbo I plan to fit to my BMW will develop the desired pressure ratio. I have determined air flow into the engine at the desired pressure ratio and have determined the rpm at which peak power and torque should arrive. I have also determined the size of...
  16. S

    How does the gear ratio affect the power efficiency generated by a wind turbine

    I have a basic question on how the power efficiency of wind turbine affected by the gear ratio. Suppose there is a generator connected with the rotor through a gear enhancer, a higher angular speed of generator is obtained. Since a higher voltage is produced, we may think that the power...
  17. J

    Lunar orbit question (calculating the mass ratio of earth and moon)

    The problem I am struggling with is this . . The centre of the Earth-Moon system is 4.7x10^3 km from the centre of the earth. Calculate; i.the ratio of the mass of the Earth with the mass of the moon. ii.The acceleration of free fall on the Moon's surface. Constants Distance between...
  18. A

    Solving the P-V Diagram Ratio of p2/p1

    Homework Statement The p-V diagram in the figure below shows two paths along which a sample of gas can be taken from state a to state b, where Vb = 4.0V1. Path 1 requires that energy equal to 3.0p1V1 be transferred to the gas as heat. Path 2 requires that energy equal to 8.5p1V1 be...
  19. T

    Optimizing Energy Efficiency through Speed Ratio Analysis

    Conserving Energy The Attempt at a Solution I started out using the above formula, but I don't understand how to get the speeds when only the masses are given.
  20. S

    Calculating the Volume Ratio of Concrete & Styrofoam for a Floating Bridge Pontoon

    Homework Statement In many locations, such as Lake Washington in Seattle, floating bridges are preferable to conventional bridges. Such a bridge can be constructed out of concrete pontoons, which are essentially concrete boxes filled with air, Styrofoam, or another extremely low-density...
  21. S

    Help finding Aspect Ratio of model plane/rocket

    Hi, I'm trying to find the aspect ratio of my model rocket-plane that I have for a horizontal flight competition for my aerospace class. It's like a rocket, with fins at the bottom, but it has two little triangular wings in the middle to stabilize it. Would I have to use a mixture of the two...
  22. L

    How to derive minimum radius ratio for a given coordination number

    Homework Statement Calculate the minimum radius ratio for CN = 3. Givens: Minimum radius ratio for CN = 4 is 0.225, so that's also the max for CN = 3. The Attempt at a Solution I know that the radius ratio determines the CN, which is related to the geometry, and that for a CN of 3, the...
  23. E

    Find the ratio of the total kinetic energy after the collision

    Homework Statement A 5.39-g bullet is moving horizontally with a velocity of +354 m/s, where the sign + indicates that it is moving to the right (see part a of the drawing). The bullet is approaching two blocks resting on a horizontal frictionless surface. Air resistance is negligible. The...
  24. T

    Compression Ratio Connection to Efficiency

    Hi. I was wondering if anyone had ever done a relationship analysis of compression ratio in relationship to efficiency. I have heard that higher compression ratio can often relate to efficiency, but I was hoping to find some kind of graph correlation on it, however I haven't been able to find...
  25. L

    Source Impedace Ratio (SIR)

    I would like to get opinions when calculating Source Impedance Ratio (SIR) on a Power System. Usually when calculating a three Phase fault it only takes into account positive sequence components, obtaining the source impedance ratio via the ratio of the source positive sequence component...
  26. J

    Velocity and distance ratio problem

    How do u show, without using calculus, that if something initially has 3 times the velocity of another object, how much farther it will travel than the other? the exact question is: A wooden block is cut into two pieces, one with three times the mass of the other. A depression is made in...
  27. S

    Which is the airfoil having highest lift to drag ratio?

    I working on a new airfoil design. Please tell me the airfoil having highest lift to drag ratio, I need it for comparison.
  28. M

    Is There a Connection Between Quantum Physics and the Golden Ratio?

    Hello, this is my first post so please be patient. I studied mathematics and have actuary qualifications. I was always obsess with the golden ratio. I was wondering if there was a relation between quantum physics and the golden ratio. A hunch told me so.
  29. S

    How to find a value for poisson's ratio

    Homework Statement The question is: A rod of 50mm in diameter and 0.8m in length is subjected to an axial load of 150kn. If the rod entends by 1.4mm and there is a decrease in diameter of 0.01mm, determine: The value of poissons ratio? Homework Equations v=lateral strain/longitudinal...
  30. M

    Simple question on Ratio of Kinetic to rest energy

    Homework Statement A pitcher can throw a baseball at 44 m/s. what is the ratio of kinetic energy to the rest energy E=mc^2. (can you use k=1/2mv^2 ?) Homework Equations rest energy=mc^2 K=gamma*mc^2 - mc^2 k=1/2mv^2 The Attempt at a Solution I am just not sure how to go about...
  31. E

    How do I calculate the ratio of charges for metal sphere?

    Homework Statement here's how the question goes: the magnitudes of the charges on two identical small metal spheres are in the ratio 5:1. the coulomb interaction force between them is F1. if they are brought into contact and then separated to their respective original positions, the coulomb...
  32. R

    What did i do wrong? Ratio and comparison test question?

    Homework Statement The summation of n/lnn from n=1 to infinity Homework Equations Ratio and Comparison test The Attempt at a Solution http://i55.tinypic.com/2jxuue.jpg Alright so the way labeled "right way" on the picture is the right way according to the book but isn't the...
  33. D

    Find half-life from an atomic ratio?

    Homework Statement An equilibrium ore mixture has an atomic ratio for \frac{U-235}{Pa-231} = 3.04x10^{6} Find the half-life of U-235 from the data. The known half-life for Pa-231 is 3.28x10^{4} years Homework Equations For secular equilibrium \frac{\lambda_{2} N_{2}}{\lambda_{1}...
  34. H

    Determining keto/enol ratio with IR

    How can you determine the ratio of the keto tautomer of a compound to its enol form? I know which functional groups are associated with which but I have no idea how you'd use an IR spectrum for quantitative analysis like this.
  35. T

    What Is the Aspect Ratio in Airfoil Design?

    in air foil : what is aspect ratio: A= b/c
  36. T

    Finding Common Ratio of Geometric Progression for 3 Points on a Parabola

    Homework Statement (p,a) , (q,b) and (r,c) are the coordinates of three points on the parabola y^2=3x. If the x-coordinate for these three points form a geometric progression whereas the corresponding y-coordinate form an arithmetic progression, find the common ratio of the geometric...
  37. P

    The skaters are pushing each other, find the ratio of their speed?

    Homework Statement Two skaters stand face to face. Skater 1 has a mass of 55 kg, and skater 2 has a mass of 75 kg. They push off one another and move in opposite directions. What is the ratio of skater 1's speed to skater 2's speed? Homework Equations KE=0.5*m*v^2 The Attempt at...
  38. I

    Explain the ratio of time scales, easy,

    Homework Statement Beta = b/sqrt(mk) Explain how Beta can be interpreted as a ratio of time scales. What do the time scales measure? b: damping coefficient of spring (dimension: M/T) m: mass attach to spring (dimension: M) k: spring constant (dimension: M/T^2) The Attempt at a...
  39. Z

    Ratio density of liquid - pressure

    Homework Statement The apparatus shown consists of four glass columns connected by horizontal sections. The height of 2 central columns B and C are 49 cm each. The height of the liquid in A and D is 52.8cm and 51 cm resp (measured from the baseline). The water columns are maintained at...
  40. N

    Solving the Difficult PDE of C1/C2 Ratio Change with Time

    Homework Statement I am trying to derive the partial differential equation for the change in the ratio (r) of two solute (C1, C2) with time during 1D flow of a reacting advecting-diffusing fluid moving through a porus media. I can define the partial differential equations for the individual...
  41. K

    Effect of Mass and Force on Acceleration and Distance Traveled in Kinematics

    [Solved] Kinematics ratio problem Homework Statement A force F produces an acceleration a when applied to a certain body. If the mass of the body is doubled and the force increased five-fold, what will be the effect on the following? a. its acceleration b. the distance the body travels in...
  42. V

    Convergence of a sequence when ratio of consecutive term converges

    Homework Statement Assume all sn =/= 0, and that the limit L = lim|(sn+1)/(sn)| exist. a) Show that if L<1 then lim sn = 0 b) Show that if L>1 then lim sn = + oo Homework Equations There is a hint that we should select 'a' s.t. L<a<1 and obtain N s.t. n>N => |sn+1 < a|sn|. Then show that...
  43. H

    Calculation of mass-energy ratio

    Homework Statement I just want to calculate the mass-energy ratio of annihilation of proton and antiproton and compare it with the observed result, e.g the mass of the two particles before annihilation and energy calculated and observed both after annihilation...I need a detailed and...
  44. S

    Calculating Surface Area to Volume Ratio for Emulsified Droplets

    Homework Statement Suppose a lipid droplet is essentially a sphere with a diameter of 1 cm. For A – D below, the area of a sphere is 4π r2, and volume is 4/3πr3. For π, use a value of 3.14. Show your calculations neatly in the space provided to receive credit for your answer. Round all...
  45. B

    Can the Li7 problem be resolved by increasing the dark matter ratio?

    Currently the WMAP results give a baryon:photon ratio of ~6.2x10-10, and a dark:baryonic mass ratio of ~5. When added to the energy density of photons + neutrinos (+dark energy at later times), the total density is then critical for a flat Universe. The BB nucleosynthesis analysis of the...
  46. E

    What's the perfect math tattoo for me?

    I've been thinking of getting a math-related tattoo, and I decided to go ahead with it, but I'm not sure what it should be. Maybe a small Euler spiral on my wrist? My mother thinks I should get the rational version of the golden ratio, but I think that'd just be lame. Thoughts please?
  47. Helios

    Solving for x: Uncovering the Golden Ratio

    If tan x = cos x, then what is x ? The answer includes the golden ratio !
  48. V

    Drag coefficient for Finite circular cylinder of low aspect ratio

    HI i have been involved with a problem which requires me to calculate the drag of a finite circular cylinder of very low aspect ratio (~1.2) i.e the h/d= 1.2 The Red= 5.4x 105 (based on diameter) and the Rex = 8.46x 106 The flow regime is very low subsonic ( M=0.15) I need to predict the...
  49. K

    Minimum % of Registered Voters Needed to Sign Petition for City Ballot

    In order to be included on the ballot in a certain city, a candidate must get at least 12.5% of the registered voters in each of three or more of the city's five districts to sign a petition. The ratio of the numbers of registered voters in the five districts is 6:5:5:4:5. In order for a...
  50. B

    Find Eb/No : signal to noise ratio

    Homework Statement If the received signal level for a particular digital system is -151dBw and the receiver system effective noise temperatyre is 1500K, what is E_b/N_o for a link transmitting 2400bps? solution says: (Eb/N0) = –151 dBW – 10 log 2400 – 10 log 1500 + 228.6 dBW = 12 dBW My...
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