Ratio Definition and 1000 Threads

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.

View More On Wikipedia.org
  1. G

    Understanding Poisson's Ratio and Restrained Cylinders

    Hey. I have a couple of questions about Poisson's ratio I hope you guys can answer. If I have a cylinder made of, let's say steel. Steel has a Poisson's ratio of roughly 0.33. The cylinder is restrained in the vertical direction so no displacement can occur. If I apply an internal pressure...
  2. B

    Breeding Ratio of thorium fuel cycle

    Homework Statement A breeder reactor is designed to work on a thorium fuel cycle. If the reactor generates a constant thermal power of 2.5GW and a production rate of 233U is 52kg per year. Find the breeding Ratio [You may assume the capture to fission ratio of 233U is 0.09 and the energy...
  3. A

    Find an expression for the mass-to-light ratio

    Homework Statement Given the luminosity profile L(r)=L0e(-r/D) and the density profile p(r) = v02/(4piGr2) find an expression for the mass-to-light ratio as a function of distance from the center of the galaxy r. Assume the ratio is unity at r = D. The Attempt at a Solution At first I...
  4. R

    No Poisson Ratio for Link Element in FEA

    in finite element analysis there is no poisson ratio for LINK ELEMENT (truss structure) just explain ?
  5. S

    Ratio of translational velocity to rotational velocity.

    1. A ball of mass m and radius R is both sliding and spinning on a horizontal surface so that its rotational kinetic energy equals its translational kinetic energy.What is the ratio of the ball’s center-of-mass speed to the speed due to rotation only of a point on the ball’s surface? The moment...
  6. Z

    Convergence or Divergence of Series with Square Roots

    Homework Statement Determine whether the series converges or diverges. \sum (\sqrt {k} - \sqrt {k - 1})^k Homework Equations The Attempt at a Solution (a_k)^\frac{1}{k} = \sqrt{k} - \sqrt{k - 1} What do I do here..? = \frac{1}{\sqrt{k} + \sqrt{k-1}} \to 0 ?
  7. A

    Refreshing gear ratio and total inertia

    Suppose we've got the setup as shown in the figure (see attachment). The idea is that the motor transfers its speed and force (rotary) to the actuator force and speed (linear) via some gears and a spindle. Here: R = radius [m] J = inertia [kg m^2] n = rotary to linear transmission [---]...
  8. M

    Ratio Test - Lim sup and lim inf version -

    Hello friends, Homework Statement lim sup |\frac{a_{n+1}}{a_{n}}| I know that this operation tests for convergence, but I don't understand how it's related to lim_{n -> \infty}|\frac{a_{n+1}}{a_{n}}| I understand that both will give the same result, but how is the latter different? lim...
  9. A

    Selectivity ratio and skirt selectivity

    Whar is selectivity ratio and skirt selectivity?? what is the -30 dB point??
  10. J

    Calculating Gamma Ratio: Tricks for Hard Problems

    Hi, I need to calculate \Gamma(7/3)/\Gamma(1/3) is there some trick to doing this type of problem? I'm finding it really hard to do from first principles. Any help would be great, thanks!
  11. Y

    Find Ratio r of R1/R2 in Two-Resistor Circuit

    Homework Statement Two resistors of resistances R1 and R2 , with R2>R1 , are connected to a voltage source with voltage V0 . When the resistors are connected in series, the current is Is . When the resistors are connected in parallel, the current Ip from the source is equal to 10Is Let r be...
  12. P

    Residue of a ratio of polynomials

    Homework Statement The problem is to find the inverse laplace of \frac{s^2-a^2}{(s^2+a^2)^2} I am supposed to use the residue definition of inverse laplace (given below) The poles of F(s) are at ai and at -ai and they are both double poles. Homework Equations f(t) =...
  13. M

    Ratio of resistance in parallel and series

    Homework Statement Two resistors R1 and R2, where R1 > R2, are connected to a voltage source with voltage V. When the resistors are connected in series, the current is Is. When the resistors are connected in parallel, the current from the source is Ip = 8.0Is. What is the ratio R2/R1? I have...
  14. K

    Can we still use the ratio test if the sequence of ratios diverges to infinity?

    Let ∑ak be a series with positive terms. Ratio test: Suppose ak+1/ak -> c. If c<1, then ∑ak converges. If c>1, then ∑ak diverges. If c=1, the test is inconclusive. What if ak+1/ak diverges (i.e. ak+1/ak->∞)? Do we count this as falling into the case c>1? Can we say whether ∑ak converges...
  15. E

    Find the ratio of maximum height to radius of planet

    Homework Statement Hint: Disregard any dissipative effects of the atmosphere of the planet. A projectile is launched from the surface of a planet (mass M, radius R) with a launch speed equal to 61 percent of the escape speed for that planet. The projectile will rise to a maximum height...
  16. F

    Proof of the Ratio Test and the Triangle Inequality

    Homework Statement Prove: If the limit inf as k goes to infinity of abs(ak+1 / ak) > 1 then the sum from 1 to infinity of ak diverges Homework Equations The Attempt at a Solution So far I have this: Suppose lim inf abs(ak+1/ak) >1 then, there exists an r such that lim inf...
  17. F

    Proof of the Ratio Test and the Triangle Inequality

    Homework Statement Prove: If the limit inf as k goes to infinity of abs(ak+1 / ak) > 1 then the sum from 1 to infinity of ak diverges Homework Equations The Attempt at a Solution So far I have this: Suppose lim inf abs(ak+1/ak) >1 then, there exists an r such that lim inf...
  18. D

    Calculating the ratio between heat capacities of a gas

    Hi, my task is to calculate the ratio (gamma) between the specific heats of a gas (Cp and Cv). The only information I have is a table of data for the pressures and volumes of the gas at different temperatures. I don't know if its monatomic, diatomic etc. (it's a later task to determine this)...
  19. C

    What is the maximum compression ratio

    what is the maximum "compression ratio" lease visit this link http://www.starrotor.com/Engines what is the maximum "compression ratio", so to speak, achievable by compressors? i don't think it is very high.
  20. J

    Charge-to-mass ratio of electron/proton

    Homework Statement The Helmholtz coil current = 2.45 A, the magnetic field = 1.91 x 10^(-3) T, the accelerating voltage = 295 V, and the beam radius = .03m. a) Calculate the e/m ratio of an electron. Show that e/m = 2V / r²B² b) During the initial use of this experiment, physicists also...
  21. M

    Calculating ratio c/a as 1.633 in HCP?

    Hi All, This is a similar post to one before, but that didn't offer much more than i know already. a = width of cell - depth of cell c= height of cell c/2 = height of central atom So i have various formula for a few isosceles lengths, namely a/2*cos30 for the base line of the vertical...
  22. C

    Finding ratio of accelerations, Ab/Aa

    Homework Statement Two astronauts are floating in space. Astronaut A's mass is 1.89 times greater as that of astronaut B. IF astronaut A pushes astronaut B, what is the ration of their accelerations, Ab/Aa. Homework Equations F=ma MaAa=MbAb (M is the mass, A is acceleration)...
  23. M

    Heat Capacity Ratio of Nitrogen for 2 Velocities

    Homework Statement This is more of a conceptual question. I understand that the heat capacity ratio is basically the ratio between the heat capacity at constant pressure to the heat capacity at constant volume. I was asked to calculate the ratio of heat capacities for Nitrogen at two speeds...
  24. J

    Aspect ratio of cylinder floating in water?

    Aspect ratio of cylinder floating in water? Hi, Basically the question is: What is the aspect ratio (h/d) for a cylinder of specific gravity 0.65 above which it will float vertically? (Note use GM = I/V - BG) So i found a solution that is simliar and can help solve the problem. (please...
  25. K

    Help with ratio 1.0 x 10-2 = 1:100

    please could you help me understand this is very simple terms. 1.0 x 10-2 = 1:100 (as in ten to the power of minus 2) i do not understand what i need to do to get it into a ratio.
  26. C

    How to Derive the Joint PDF Using the Ratio of Uniforms Method?

    Hi everybody: I am trying to solve this question: [PLAIN]http://imageshugger.com/images/wviidazp3mf06ej32.jpg I have made the following: u=y v=xy Calculated the Jacobian, which is |-y|=y then as I know that is unnormalized I need to normalized first using a double integral as a...
  27. C

    Consider a transformer with winding ratio of 1 : 10

    Just out of curiosity : Consider a transformer with winding ratio of 1 : 10. What happens when AC 120 v is applied on primary and on secondary we apply DC voltage of 120 v from a battery source is series or in parallel? What will be the output in both cases?
  28. A

    Ratio for Kindetic and Potential energy

    If the phase angle for a block-spring system in SHM is φ and the block's position is given by x = xm cos(ωt+φ), what is the ratio of the kinetic energy to the potential energy at time t = 0? State your answers in terms of the given variables. x =xm Cos(wt + phi) v = -w(xm)sin(wt +phi)...
  29. K

    How Do You Calculate Pressure Ratio After Multiple Pump 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...
  30. N

    Signal to interference ratio for CDMA

    Hi, I am doing a project on communications engineering. I've done some background reading on CDMA and spread spectrum technologies such as Direct Sequence and Frequency Hopping. My project supervisor has asked me to find out the equation for the signal to interference ratio of CDMA systems...
  31. F

    The ratio of two total differentials equals the dervative? Why?

    I was stuck on a problem in my Diff Eq book and I asked my teacher for some guidance. This was the problem: Let M dx + N dy = 0 be a homogeneous diff eq. Using the substitution y = r sin(t), x = r cos(t), show that this equation is a separable equation of r and t. Now it was obvious that...
  32. L

    Gear ratio and power output in a car

    I'm a bit confused about power output and gear ratios. I think it's best to explain by going by my example (imperical units, sorry Americas & Brits): Mass: 1300kg max. power: 128 kW @ 5500 rpm max. torque: 245 Nm Gear ratios (from a slightly different car type, but should be similar): 1st...
  33. E

    Determining convergence of infinite series with factorial without ratio test

    Homework Statement Determine whether the series below is convergent or not: \sum 7*\frac{n!}{n^{n-10}} n=8 and the series goes to infinity (Sorry, I couldn't get the formatting correct.) Homework Equations n/aThe Attempt at a Solution Well, originally I thought the series was divergent...
  34. P

    Rigorousness of derivatives as ratio of differentials

    Homework Statement I have often heard that given say, ds/dt=k, that it is not entirely rigorous to say that ds=kdt. Why is that? If I view the derivative as nothing more than a ratio of the differentials, that seems perfectly reasonable. Also I see this done all the time, with acknowledgment...
  35. E

    Elastic reactions, ratio of cross sections

    Hello everybody, I am having some troubles with this exercise. I have attached the text and the solutions to my post. My problem is, after I have coupled the angular momenta and used the CK coefficients like in (|\pi ^{+}p>=|1,1>|1/2, 1/2>=|3/2,3/2>) (pag.432) I don't understand what...
  36. E

    Flow Rate Ratio of Two Tubes: Calculation

    Homework Statement Two tubes carry the same incompressible fluid with viscosity 1.5 Pl. They have lengths L1 = 6 and L2 = 22 m and diameters d1 = 1.2 and d2 = 4.5 cm. What is the ratio of their flow rates F1/F2? Homework Equations Poiseuille's law: 8nLI/(pi*r^4) while n is viscosity L...
  37. D

    Ratio of Kinetic to Potential Energy of Simple Harmonic Oscillator

    Homework Statement Calculate the ratio of the kinetic energy to the potential energy of a simple harmonic oscillator when its displacement is half its amplitude. Homework Equations KE=1/2mv2 = 1/2kA2sin2(wt) U=1/2kx2 = 1/2kA2cos2(wt) KEmax=1/2kA2 Umax=1/2KA2 The Attempt at a...
  38. M

    Charge-to-Mass Ratio of Electron in Circular Path

    electron is deflected in a circular path electron speed = 2.7 x 10^8 m/s diameter = 3cm magnetic field = 0.24T 1. work out charge to mass ratio - 7.5 x 10^10 2. the textbook value is 1.76 x 10^11 - comment on this value The answer is given as electron traveling close to speed of...
  39. M

    Phi (1.6) Found at Quantum Level: Major Breakthrough?

    So I've read that phi (1.6) has been found at the quantum level, and from what I've been told this is a major breakthrough. But I fail to see the relevance. I was wondering if anyone felt that this is a major breakthrough, and could explain this to me? edit: posting link to article...
  40. G

    Help with Ratio: Mr Smith & Mr Jones 24:9

    Here is a problem involving ratio , and the answer plus work as given by my textbook. I get a little lost at the underlines part. I don't understabnd how we arrived at a ratio of 24:9. Can anyone help me out? Mr Smith starts a business with $50,000. 3 months later, Mr Jones joins the...
  41. J

    Why Do We Use the Ratio of Favorable to Possible Outcomes in Probability?

    Why do we take the "probability of an event" ratio as favorable / possible outcome If A is an event, then probability that A will occur is given by P(A)= no. of favorable outcomes / total no. of possible outcomes Is this just a definition, or is there some special significance in taking...
  42. D

    Why is Muon Charge Ratio Positive?

    Hi, Could anyone explain to me why it is that cosmic radiation supplies slightly more positive than negative muons? I know that negative muons disappear a little faster than the positive ones as they can decay or be captured, but I don't know if this would have any impact on what I'm asking...
  43. J

    Heat capacity ratio for diatomic gases

    Calculate the heat capacity ratio for a diatomic ideal gas. ---- Using the equipartition theorem, I calculate: Cp / Cv = (Cv + R) / Cv = (7/2 R + R) / (7/2 R) = (9/2 R) / (7/2 R) = 9/7 ~ 1.286 According to the equipartition theorem, I assign each vibrational degree of freedom 1 R and...
  44. B

    Why is the dark matter: baryonic matter ratio about 5:1?

    All the LCDM models with variations (see http://lambda.gsfc.nasa.gov/product/map/current/parameters.cfm ) have similar ratios of dark matter: baryonic matter density of very close to 5:1. Is this ratio determined from WMAP data such as angular size of a peak, or is it a not very tightly...
  45. I

    How Can Poisson's Ratio Reach -1?

    v = \epsilontrans/ \epsilonaxial where ν is the resulting Poisson's ratio, \epsilontrans is transverse strain \epsilonaxial is axial strain and Poissions Ratio have range and its not more then 0.5 and not less then -1? so my question is how its value can turn "-1"? As...
  46. R

    Ratio of functions, surjective (analysis course)

    Homework Statement let f: R->R be a continuous function Suppose k>=1 is an integer such that lim f(x)/x^k = lim f(x)/x^k = 0 x->inf x->-inf set g(x)= x^k + f(x) g: R->R Prove that (i) if k is odd, then g is surjective (ii) if k is even, then there is...
  47. B

    Electromagnet coil core to yoke ratio?

    I'm building pairs of coils with standard core heights and diameters and linking each pair with a yoke. The magnets all run at 6V DC with windings of 24 AWG magnet wire in 6/8/10 layers. Is there a ratio of coil core mass to yoke mass for maximum efficiency? (shown below)
  48. S

    What substance has the highest expansion ratio?

    What substance has the highest expansion ratio? (liquid:gas)
  49. T

    Charge-to-mass ratio with Zeeman Effect

    Homework Statement I'm supposed to determine e/m using Zeeman effect. B=0.45 T Difference between two spectral lines is also known (0.649x10^10 Hz)Homework Equations Normal or anomalous Zeeman effect? How you know it? I'm guessing normal, so \Delta E = m_{l} \frac{e \hbar}{2m_{e}}B \Delta E =...
Back
Top