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
Recent contents Top users
  1. G

    Signal to Noise Ratio Between Spacecraft Transmitter and Receiver Antenna

    Homework Statement Determine the SNR for the spacecraft that uses a transmitter power of 16 W at a frequency of 2.4 GHz. The transmitter and receiver antenna gain are 28 dBi and 60 dBi, respectively. The distance from the space- craft to ground is 2 ϫ 1010 m, the effective noise temperature...
  2. 1

    Proving a=b=c in a Ratio Proportion Problem

    Homework Statement if(i have attached the equation's pic) then prove a=b=c or (a+b+c)(x+y+z)=ax+by+cz Homework Equations if a/b=c/d=e/f each ratio = (a+c+e)/(b+d+f) The Attempt at a Solution I was able to prove (a+b+c)(x+y+z)=ax+by+cz like this: each ratio=...
  3. B

    Calculating the ratio of charges in Leyden Jar

    Hello In Walter Lewin's lecture while explaining the Leyden jar he says that the charge on the glass is 12 times more than that in the air gap. How is this obtained ? Basically there are 2 metal containers separated by a glass sheet. The air gap between the outer conductor and glass is 1...
  4. D

    Circular motion time/radius ratio question

    Homework Statement 16. A car completes a horizontal circle of radius r in time T. The same car then completes a larger horizontal circle of radius 2r in half the time. What is the ratio of the centripetal acceleration ac for the car in the second circle to that in the first circle a c2 a c1...
  5. L

    Carrier Swing & Deviation Ratio: Clarifying the Definitions

    Can anyone help me to find out the definition of "carrier swing"&"deviation ratio"? The definitions which i found on surfing the net is too vague.Can someone help me with this?
  6. A

    Formula for RoR with ROI and Capital to investment ratio.

    Capital=All of your money. Investment= Portion of your money invested per unit ( day/month/hand/game) RoR= Odds that you will go broke RoR@X= Odds that your Capital will be less than Unit of Investment before reaching X. ROI= Return on investment, measured by percentage per...
  7. T

    Does Changing the Idler Diameter Affect Record Player Speed?

    I'm new to this site so excuse me if I'm posting in the wrong area. We are having a discussion about motor, idler pully (yes wheel) ratios and we can't agree on this problem. What we have is basically an old record player, The motor shaft is turning a single idler, and this idler is...
  8. U

    Damped oscillator consecutive amplitude ratio

    Homework Statement Undamped oscillator's period T_0 = 12s. Damped oscillator's angular frequency \omega_1 = \omega_0 * 97\% where \omega_0 is the angular frequency of the undamped oscillator's. What is the ratio of consecutive maximum amplitudes? Homework Equations Equation of damped...
  9. Ƒ

    Molar Ratio Problem: Find Ethane to Methane

    Homework Statement Unknown amounts of methane and ethane are mixed at STP. The resulting mixture has a density of 1.18 g/L. Find the ratio of ethane to ethane. The Attempt at a Solution Since it's a ratio, we can convert it to 1 mol methane : X mol ethane 1 L methane at STP = \frac{RT}{P} =...
  10. M

    Using Ratio Test to Decide Convergent/Divergent

    Homework Statement The Attempt at a Solution I got that the limit goes to infinity using the Ratio Test and that would mean B. But I'm not 100% percent sure. Just looking for some to verify my answer if I'm correct or not.
  11. T

    Using ratio test to find radius of convergence

    Homework Statement Ʃ((x-3)^(n)) / (n*2^(n)) Homework Equations lim as n→ ∞ (An+1 / An) The Attempt at a Solution When dividing two fractions, invert the second and multiple to get what you see below. (x-3)^(n+1)/((n+1)*2^(n+1)) * (n*2^(n))/((x-3)^(n)) Do some cross...
  12. X

    Cube beam splitter transmission and reflection ratio

    Looking around at all the cheap surplus beam splitter cubes out there. I've found no description of how things would be expected to behave outside of the spectral bands for which they're designed. Leaving out the transmissivity of the glass itself, should I assume that when relative...
  13. S

    Log-Likelihood ratio in the context of natural language processing

    First of all, let me apologize if this question is in the wrong place. It's fundamentally a statistics question but it relates to computer science. I'm also not sure if this falls under the "homework" category, since it's for a class, but I need assistance on a general idea, not a problem set...
  14. S

    Classical Physical Explanation for Turn Ratio in Transformer

    Hello. I'm trying to understand why, in terms of Maxwell's Equations, the ratio of the number of turns in a transformer converts an input voltage to an output voltage. EE explanations only seem to go as deep as this article: http://en.wikipedia.org/wiki/Transformer#Basic_principles They state...
  15. T

    Fresnel Lens Concentration Ratio

    Homework Statement Hey guys, I am part of a group building a solar oven. It will consist of insulated sides and a glass window on the top. Rather than using reflectors we want to salvage a Fresnel lens from an overhead projector to concentrate sunlight onto the glass window. Part of the...
  16. S

    Dalton's law of partial pressures equivalent to volume ratio?

    Homework Statement I had a general inquiry about a relation in my physical chemistry textbook. It stated that when determining the partial pressure of an ideal gas component in a mixture/solution, instead of using the standard Dalton's law: Pi = xiPtot, one can simply use the relation Pi =...
  17. L

    Estimating the damping coefficient of a wave assuming a very small ratio

    Homework Statement The original problem is determining the dispersion relation of an ordinary wave in plasma damped by collisions. That part was easy enough but the next part is to find the damping rate (-Im(ω)) of the wave, assuming k is real and \nu << \omega where \nu is the collision...
  18. N

    What method is more accurate to find the turns ratio?

    Which method of determining turns ratio is more accurate and why? 1. From the voltage readings in no-load condition 2. From the current reading in loaded condition We used an auto transformer (VARIAC) to supply voltage to a single phase transformer. Supplied voltage was 220 V. Then we...
  19. K

    A/F Ratio & BSFC: Q&A to Understand Effects

    I have few questions as i am bit confused Q1. I want to know what are the influence of the air/fuel ratio on engine output and Brake specific fuel consumption (BSFC). Q2. why bsfc increases at low engine output? Q3. why bsfc improves as engine output increases? Q4. what are the...
  20. A

    Diffraction Grating Overlapping Orders

    Homework Statement The same diffraction grating is used with two different wavelengths of light, λA and λB. The fourth-order principal maximum of light A exactly overlaps the third-order principal maximum of light B. Find the ratio λA/λB. Homework Equations sin theta = m lambda /...
  21. Rapier

    Using the Ratio Test Methodology to Determine Convergence

    Homework Statement Determine whether Ʃ(1→∞) n^2/e^n converges or diverges. Homework Equations L = lim (n→∞) abs [a_n+1/a_n] The Attempt at a Solution The prof was out of town so left us a "self-study" task. We're looking at the Ratio Test and I want to see if my methodology is...
  22. L

    How Can I Calculate the Weight a Gear Reduction System Can Lift?

    Hi, I'm new to this forum but I've read over probably a dozen threads so I figured that someone should probably be able to help me; please forgive me if this is the wrong area to post this question as well. Dilemma: So the problem right now is that I'm trying to use a gear reduction system...
  23. B

    Water Poisson Ratio: What & How?

    hello everybody. can we define a poisson ratio for fluids, eg for water?? if no, why? n if yes, how?? thnx.
  24. B

    Need help w/ Fibonnaci and Golden Ratio proof

    Let F_n and F_n+1 be successive Fibonnaci numbers. Then |(F_n+1)/(F_n) - Phi | < 1/(2(F_n)^2) Where Phi is the Golden ratio.
  25. C

    Quite a tricky gear ratio question to ponder

    If a 6 speed gear box has a 1st gear ratio of 7:1 and a sixth gear ratio of 1:1 how would you calculate the 2nd,3rd,4th and 5th gear ratio's? If you use the equation for geometric progression which was my first thought - it doesn't work! Any ideas?
  26. T

    Proton electron mass ratio calculation

    Homework Statement Hello! I've come upon this question and haven't been able to find it anywhere. The goal is to find Mp/Me with basis on the Bohr's atomic model and hydrogen emisson spectrum lines.Homework Equations l=rp=nh_ ; h_=h/2pi ; E=-K.e^2/2r ; r=(n^2.h_^2)/Me.e^2.k ...
  27. S

    Inelastic Collisions and ratio of their masses

    Homework Statement Two objects moving in opposite directions with the same speed undergo a totally inelastic collision, and half the initial kinetic energy is lost. Find the ratio of their masses, m1/m2. Homework Equations m1v1+m2v2=(m1+m2)vf The objects are moving in opposite directions...
  28. R

    Temperature ratio across normal shockwave

    Homework Statement Consider a stationary normal shock wave in pure diatomic nitrogen. The velocity and temperature upstream are known. Calculate the temperature ratio across the shock, assuming local thermodynamic equilibrium. Neglect any chemical reactions and electronic energy...
  29. B

    The ratio of strength between electro magnetic and gravitational force

    In stenger's book he claims that the ratio between gravity and the electro magnetic is not 1039 Let me know if you think he's right Note that N1 (ratio of EM force to gravity) is not a universal number; it depends on the charges and masses of the bodies you use in the calculation. For an...
  30. R

    How Do You Solve Complex Ratio Problems in Chemistry?

    Homework Statement In each of the following the properties of a compound are given. In each case find A:B:C 1. 3/8 of A with B and C 1:2 2. A, B, C are mixed according to the ratios A:B=1:7 and B:C=13:9 Homework Equations The Attempt at a Solution I just can't seem to...
  31. M

    A limsup inequality (showing that the root test is stronger than the ratio test)

    Homework Statement Show that if a_n > 0 for all n, \liminf{\frac{a_{n+1}}{a_n}} \leq \liminf{a_n^{1/n}} \leq \limsup{a_n^{1/n}} \leq \limsup{\frac{a_{n+1}}{a_n}}Homework Equations \liminf{a_n^{1/n}} \leq \limsup{a_n^{1/n}} \liminf{\frac{a_{n+1}}{a_n}} \leq \limsup{\frac{a_{n+1}}{a_n}} These...
  32. I

    Finding force exerted by a rope and ratio of tension:weight

    Homework Statement A 72.8 kg ice skater is moving at 5.01 m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius 0.765 m around the pole. The acceleration of gravity is 9.8 m/s2 . Find the force exerted by the rope on...
  33. C

    Photons vs neutrinos energy ratio

    What is the ratio of energy contained in photons vs energy contained in neutrions in the present universe? Also, how is that ratio changing with time? Thanks.
  34. K

    Ratio of logarithms in various bases to other bases

    I'm unsure as to if I am using the correct terminology, but what I mean by this is log = logarithm in base 10. ln = logarithm in base e. logx = logarithm in base x. Upon some investigation, I found that log(a)/ln(a)=log(b)/ln(b) where a and b are constants, meaning that there is a ratio...
  35. C

    Calculating ratio energy radiated in a loop and comment on result

    Homework Statement Designers of electrical circuits often take the maximum amplitude of the radiated electric field (at a large distance r) produced by an alternating current I0 flowing in a loop of area A cm2 to be given by E=\frac{2.6AI0f2}{r}\muVm-1 where f is the frequency in MHz...
  36. B

    Determining Series Convergence using the Ratio Test

    Homework Statement I'm asked to specifically use the Ratio Test (formula below) to determine whether this series converges or diverges (if it converges, the value to which it converges is not needed.) \sum_{n=1}^{\infty}\frac{n}{(e^n)^2} Homework Equations Ratio Test: If a_n is a sequence...
  37. O

    Angle Between Vectors given Ratio of Resultants, why is this wrong?

    Homework Statement Vectors A and B have the same magnitude. Given that the magnitude of A + B is 75 times greater than the magnitude of A - B, find the angle between them? Homework Equations We know that A=B, so: 2AB+2ABCos\theta=75(2AB-2ABCos\theta) Given that A=B...
  38. L

    Convergence of series using ratio test

    Homework Statement assume summation of series An converges with all An>0. Prove summation of sqrt(An)/n converges Homework Equations The Attempt at a Solution I Tried using the ratio test which says if lim as n goes to infinity of |Bn+1/Bn|<1 then summation of Bn converges. I let Bn...
  39. R

    How do you solve ratio problems like these?

    Homework Statement In each of the following the properties of a compound are given. In each case find A:B:C 1. 1/5 of A, 2/3 of B and the remainder of C. 2. 3/8 of A with B and C in the ratio 1:2. 3. A, B and C are mixed according to the ratios A:B= 2:5 and B:C=10:11. Homework...
  40. R

    Signal to Noise ratio dB levels

    Hello, I have some 10 signals in noisy and nonoise(noisy+good) situations. I just calculated the power of each signal in two cases and then used SNR formula for dB(10log noisy/nonoise). Now, I got noise levels in dB's. Here, i confused that these dB levels are referred to...
  41. G

    Hydration energy and charge to size ratio of ions

    why does the hydration energy decrease as the size of the ion increases? I want a logical reason... I already know that it is because the charge to size ratio decreases...
  42. M

    Chemistry Calculating 100ml with a mole vs mole ratio

    Homework Statement I have pure ethanol and water. When mixed, the total volume is not the sum of the individual volumes (its a little bit less). A wikipedia graph has shown that a 0.4mol ethanol to 0.6mol to water mixture is ideal to get the most contraction...
  43. A

    Minimum Critical Power Ratio (MCPR) for a BWR

    From Todreas & Kazimi, Nuclear Systems I, Problem 2-3 1. Homework Statement Calculate the minimum critical power ratio for a typical 1000 MWe BWR operating at 100% power using the data in Tables 1 – 2, 1 – 3, and 2 – 3. Assume that: a) The axial linear power shape can be expressed as...
  44. S

    Selecting the Right Transformer Turns Ratio for a Given Voltage

    Considering a practical transformer, We can get a given voltage and corresponding current ratio by selecting a particular turns ratio. ie. V1/V2=N1/N2=i2/i1 Say that I want to make a 240V/60V. Now 240/60 volts ratio can be acheived by considering different no. of turns on primary(P) and...
  45. T

    Finding the damping ratio (zeta) of an nth order system from a transfer function

    I am having trouble with some of my homework. I am not quite sure how to find the damping ratio from a third order system when the transfer function (of s) is the only information supplied. Could anyone help me with this? I would like a method that would work with any nth order system...
  46. N

    Electronic Signal and System problem: Ratio of signal energy

    Homework Statement x(t) is input into a perfect lowpass filter with frequency response H(ω), having a bandwidth of BHz and a passband gain of 1. For B = (2πT)-1 Hz, calculate the ratio of the output signal energy to the input signal energy. Homework Equations x(t) = Ae-|t|/T The...
  47. N

    Electronic Signal and System problem: Ratio of signal energy

    Homework Statement x(t) is input into a perfect lowpass filter with frequency response H(ω), having a bandwidth of BHz and a passband gain of 1. For B = (2πT)^-1 Hz, calculate the ratio of the output signal energy to the input signal energy. Homework Equations x(t) = Ae^-|t|/T The...
  48. L

    Working out the sides on a die and the numerical ratio on the die

    Being a hobbiest programmer, I know enough about probability to get by. However, I've set myself an impossible (for me) calculation in my current personal project. I have a set of numbers. For this particular problem it is a set of four numbers {248, 184, 120, 56}, but I'll be repeating the...
  49. N

    Mass to Light Ratio for Dwarf Galaxies

    Hi, I'm working on a project on dwarf spheroidal galaxies. Is there a way to get a mass-to-light ratio knowing the distance to the galaxy, its size, and maybe some other parameters like the absolute magnitude or velocity dispersion? In the end, I'm trying to figure out their masses using...
  50. S

    Steel - Youngs Modulus, Poisson Ratio

    Hello, Quick question on how you would go about calculating this. A grade of steel has the following properties; Tensile strength = 300 N/mm^2 - (not relevant?) Youngs Modulus = 200 GPa Poisson Ratio = 0.3 The grade of steel is 2m long, with a 20mm cross sectional area. It is positioned...
Back
Top