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. Z

    Ratio & Root Tests: Convergence & Divergence

    Homework Statement Test for convergence and divergence. Homework Equations \sum_{i=1}^{n} \frac{n!}{3^n} \sum_{i=1}^{n} \frac{1}{{(log (n))}^{1/n}} The Attempt at a Solution For the first one I get \frac{(n+1)}{3} After applying the ratios. Taking the limit as n approaches infinity, it is...
  2. M

    Fibonacci Sequence Ratios: F_n+1/F_n

    The sqeuence of ratios of a fabinacci number F_n+1/F_n on looking at this. F_2/F_1 =1/1 =1 F_3/F_2 =2/1 =2 F_4/F_3 =3/2 =1.5 F_5/F_4 = 5/3 = 1.667 Why would F_n+1 = at F_4 =3 with also F_3=2 I think i understand the squence is fabin accie on the denominater but on the...
  3. N

    Find Signal to noise ratio (SNR)

    has a transfer characteristic |H(f) given in the link below. The transmission is at maximum error-free rate of 4,800 bps. Compute the SNR (signal-to-noise-ratio) at the channel output. Does the output signal suffer from any distortion? http://imageshack.us/photo/my-images/263/79465468.jpg/...
  4. D

    Properties of the super-golden ratio?

    The Supergolden ratio is the solution of x3=x2+1. \psi = \left({{\sqrt{31}}\over{2\ \times 3^{{{3}\over{2}}}}} {{29}\over{54}} \right)^{{{1}\over{3}}} {{1}\over{9\,\left({{\sqrt{31}}\over{2\ \times3^{ {{3}\over{2}}}}} {{29}\over{54}}\right)^{{{1}\over{3}}}}} {{1}\over{ 3}}\approx...
  5. D

    Trignometric and hyperbolic equalities: Why the golden ratio?

    1. \sin \theta = \cos \theta \theta=\frac{\pi}{4} 2. \sin \theta = \tan \theta \theta = 0 3. \cos \theta = \tan \theta \theta =\arcsin (\varphi -1) 4. \sin \theta = \csc \theta \theta = \frac{\pi}{2} 5. \sin \theta =\sec \theta \theta does not exist. 6. \sin \theta =\cot...
  6. P

    Calculating the Ratio of Planet Masses Using Newton's Law of Gravitation

    Homework Statement The weight of an object of mass 1kg at the surface of Mars is about 4N. The radius of Mars is about half the radius of Earth. Estimate the ratio: mass of Mars/Mass of Earth Homework Equations The Attempt at a Solution The answer is 0.1 but I don’t see...
  7. L

    Determining baseband S/N ratio and link margin for a satellite link

    Hi everyone, I'm not sure if this is the right section to post this in, but the question doesn't really seem to fit any singular category, so I'll try this one (if someone has a better recommendation, please let me know!) The question I'm seeking to answer is this: A baseband signal of...
  8. R

    Hacked off with college over Velocity Ratio and Efficiency question.

    Homework Statement If the work put in is 3000j, calculate the useful energy output. [PLAIN]http://www.mkwebman.com/question Load = 1962N Homework Equations VR = Distance covered by effort / Distance covered by load MA = load/effort Efficiency = MA / VR Efficiency = useful...
  9. K

    Carrier-to-Noise Ratio Question

    Homework Statement A receiving system consists of an antenna with an effective noise temperature of 70 K. This antenna is connected to a microwave front end of noise figure 7 dB via a feeder. The feeder’s specific attenuation function is 0.2 dB/10m. The actual feeder length is 2 m. Calculate...
  10. K

    What is Image Rejection Ratio (IRR)

    What is Image Rejection Ratio (IRR) and How to calculate an Image Rejection Ratio (IRR)?
  11. E

    Using Gravitational Force Equilibrium to Calculate M2/M1 Ratio

    Homework Statement Here is the objective: To experiment with the resultant of two gravitational forces. In particular, you will find the equilibrium position for a test mass located on a line between two point masses. Here are the instructions: (1) Drag the test mass (red disk) to an...
  12. Saitama

    Ratio of Copper Valencies in Oxides

    Homework Statement Copper forms two oxides. For the same amount of copper, twice as much oxygen was used to form the first oxide than to form the second one. What is the ratio of the valencies of copper in the first and second oxides? (This is not my homework question. I am solving a book...
  13. T

    Find the ratio (ideal gas laws) how to get a Ratio between two numberS>

    Homework Statement The temperature of a fixed mass of gas drops from 127 C to 27 oC under constant pressure. Find the ratio of the new volume to the original volume. C. 3:4 D. 4:3 E. 1:1 A and B arent here because i have gotten them wrong. Homework Equations Ideal gas law: PV=...
  14. B

    Calculating Mass Ratio in Collision of Two Carts

    Two carts each 12 cm long travel toward each other on a frictionless air glider track. The first cart on the left has an initial velocity of 18 cm/s toward the other cart that is stationary. The carts then collide. The cart on the left has a new velocity of -4cm/s and the stationary cart now has...
  15. K

    Is There an Ideal Height to Diameter Ratio for Neo Magnets?

    I am working on a project that will use cylindrical neo magnets. Is there an ideal height to diameter ratio for neo magnets?
  16. C

    Root test vs. ratio test question

    I am doing the following practice problem in prep for an exam: sum from n=0 to infinity: (3^n)/(n+1)^n The book says to use the ratio test on it, which I did, but would the root test also apply to this?
  17. M

    Proving convergence of factorial w/o Ratio Test

    Homework Statement Determine whether 1/n! diverges or converges. So far, we have only learned the comparison tests, p-series, geometric series, divergence test, and integral test, so I can only use these tests to prove it. Homework Equations N/a The Attempt at a Solution I...
  18. R

    Speed as a ratio, but what about work done and moments?

    Hi all, Speed is a ratio of the distance traveled per unit time. But what then is work done and moments? For example, work done is force multiplied by the distance traveled in the direction of the force. But how would you explain the rationale of multiplying these two quantities? As...
  19. B

    Calculating Poisson ratio is a way to measure a material's response to stress.

    Homework Statement question A ciclindrical metal specimen 10 mm in diameter is stressed elastically in tension. A force of 15000 N produces a reduction in diameter of 0.007 mm. Compute Poisson ratio if its elastic modulus is 100 GPa Homework Equations E=stress/strain The...
  20. B

    How to Compute Poisson Ratio Correctly?

    question A ciclindrical metal specimen 10 mm in diameter is stressed elastically in tension. A force of 15000 N produces a reduction in diameter of 0.007 mm. Compute Poisson ratio if its elastic modulus is 100 GPa my attempt D original = 0.01m change in D = 0.000007m F=15000N E=...
  21. L

    Neper freq, Damping factor, ratio, coefficient confusion.

    Hi all, this is my first post. I find a lot of conflicting definitions of damping factor, damping coefficient, and damping ratio on the internet, and in some textbooks, when related to RLC circuits. Sometimes I see the neper frequency described as the damping factor or damping coefficient...
  22. 5

    Charge to Mass Ratio of a Particle to Electron - Mass

    Homework Statement To start, I did find a few very similar or equal topics, but I could not gather enough information. And, the pi symbols are intended to be pi symbols with negative superscripts (couldn't get it to work/finalize). --- The charge-to-mass ratio of a \pi- particle is known to...
  23. S

    Ratio volume of cylinder inside cone

    Homework Statement Show that the volume of an upright cylinder that can be inscribe in an upright cone is 4/9 times the volume of cone Homework Equations volume of cone volume of cylinder differentiation ?? similarity of triangle The Attempt at a Solution I draw the picture of...
  24. P

    Find K/Ug: Solving a Constant Ratio of Kinetic and Potential Energy

    I don't really know how to approach this problem... A satellite is in a circular orbit around its parent body. The ratio of the satellite's kinetic energy to its potential energy, K/Ug, is a constant independent of the masses of the satellite and parent, and of the radius and velocity of the...
  25. D

    Solving Ratio Test Limit with x and -3

    \begin{array}{l} \\ \mathop {\lim }\limits_{n \to \infty } \left| {\frac{{{x^{n + 1}}\left( {\frac{1}{{{{\left( { - 3} \right)}^{n + 1}}}} - 1} \right)}}{{{x^n}\left( {\frac{1}{{{{\left( { - 3} \right)}^n}}} - 1} \right)}}} \right| = \mathop {\lim }\limits_{n \to \infty } \left| {\left(...
  26. B

    Ratio magnetic induction between 2 solenoids

    We have 2 solenoids : S1 and S2 The coils are wind up as close as they can get and both have length L. They are both made from the same material and have the same length. They are both connected to a DV source. S2 has a wire with a double diameter The ratio between B1 and B2 then is? I...
  27. A

    Magnetic Moment to Angular Momentum Ratio

    Homework Statement Suppose that an electron is a small spherical shell of mass m with a charge e spread over its surface. Show that the ratio of the magnetic moment to angular momentum of such an electron should be e/2m whether the electron is a) moving in a circular orbit or b) spinning...
  28. A

    Velocity Ratio of a 3rd Class Lever

    Homework Statement 1962N Load 5 m from effort (hydraulic ram) and fulcrum 1m from effort. Calculate the Velocity ratio, if work input is 3000j calculate work output. Homework Equations VR = distance moved by effort / distance moved by load effort = 11772N MA = load / effort =...
  29. DaveC426913

    Age Ratio of Ship and Boiler

    The ship is twice as old as the boiler was when the ship was as old as the boiler is. What is the ratio of their ages? I do believe I have solved this (without Googling) and have uploaded my answer online with a timestamp of 10:35PM 4/27/2011 (i.e. before I posted this). Let me know...
  30. A

    How do I calculate percentage increase for ratios in math homework?

    Homework Statement 1. A photocpier increases the paper with the ratio 4:5, what % is the paper increased 2. An alloay has a copper, alloy and lead with the ratio 5:7:3, what % is the alloy to lead 2. The attempt at a solution 1. Difference in equation = 5 - 4 = 1...
  31. A

    Conduction to Displacement Current Ratio

    Homework Statement For copper we find that J=\sigmaE , where \sigma has the value 5.8x10^7 mksc units. If an alternating electric field represented by E0ei\omegat exists within the copper. Find the ratio of the conduction to the displacement current density at a frequency of 1megacycle/sec...
  32. A

    Mass ratio of steam-ice mixture

    Homework Statement Ice cube at 0 degree is mixed with steam at 100 degree, both become water at 50 degree. Find the ratio of mass of the ice : mass of steam Homework Equations Q=ml Q=mcdT The Attempt at a Solution I tried this way : let the ratio of ice to steam = a:b a x...
  33. C

    Effect of ratio of energy density of matter and radiation on redshift

    Homework Statement If the ratio of the energy densities of matter and radiation was much higher than it is today (by several orders of magnitude), in a few sentences describe what effect this would have on the redshift (or scale factor) when the universe switched from being...
  34. P

    As temperature of a conductor increases why does the ratio of

    as temperature of a conductor increases why does the ratio of conductivity to resistivity increase ?
  35. A

    Ratio of rates (e+ e- -> mu+ mu-)

    Homework Statement For e^+ e^- collisions at \sqrt{s}=5 GeV, estimate the ratio of the rates at which interactions produce hadrons and \mu^+ \mu^-Homework Equations \sqrt{s} = 2E = E_{cm} \Gamma = \frac{S |p|}{8 \pi \hbar m_1^2 c} |M|^2 where M is the matrix element \frac{d \sigma}{d...
  36. M

    Calculate Mass of Eri B & C: Solar Mass Ratio

    Homework Statement we are looking at two stars in the eridani system, eri B and eri C. the period of the system is 247.9 years. the system's measured trigonometric parallax is 0.201 arcseconds and the tru angular extent to the semimajor axis of the reduced mass is 6.89". the ratio of...
  37. U

    Moderator to fuel ratio and under-moderation in different lattices

    Hi all. I need help on an issue I can't figure out. What is the difference between 15x15 and 17x17 fuel when it comes to moderation properties? Standard fuel with these lattices have dimensions 15x15: pitch: 14.3 mm, d_rod: 10.77 mm 17x17: pitch: 12.6 mm, d_rod: 9.5 mm These geometries...
  38. S

    Determining Theta in Sin Ratio: Why the Difference?

    Homework Statement The ratio sin theta =-12/13 Homework Equations The Attempt at a Solution which comes out to according to my calcuations -0.9230, i then use 2nd sin function on my calculator and come up with -67.3 degrees this answer is legitimate but another way of writing...
  39. K

    How do you construct the pattern of a dragonfly wing using the golden ratio?

    You can see it here starting at 2:30 https://www.youtube.com/watch?v=http://www.youtube.com/watch?v=kkGeOWYOFoA My question is, how do you determine the position of the points used to draw the triangles and circles.
  40. B

    What Was the Ratio of Quarks to Antiquarks in the Early Universe?

    Martin Rees in his book Just Six Numbers says that in the early universe there 1 billion antiquarks and a billion and one quarks. Is that really known? How is known what the ratio of antiquarks to quarks was?
  41. O

    Approximate Ratio: Steps to Find Reasonable Solutions

    The following is an approximation problem. Given a ratio: D =\frac{ \sum a_ib_i}{\sum b_ib_i} I wonder what steps to follow to give a reasonable approximation. This is an intuition D =\frac{ \sum a_i}{\sum b_i}. Clearly, given that all b_i terms are the same, the approximation is the...
  42. A

    Thrust to weight ratio and lift

    hello a plane would need a thrust to weight ratio of 1 of fly straight up without losing speed but how can a plane in level flight maintain its altitude with <1 TWR since to maintain a level flight you need to have lift = weight so your engine needs to supply enough power to generate...
  43. J

    What does the ratio c/a mean in solid state phyiscs

    What does the ratio c/a mean in solid state physics? I have attached a table with a an example. Cheers
  44. S

    Plotting Mach number as a function of Area ratio

    Homework Statement A=0.1+x^2 in a convergent -divergent nozzle .I need to plot mach number as a function of x for isentropic flow across the nozzle. I know the A/A* as a function of Ma. But finding the opposite (Ma in terms of A/A*) from that equation did not seem to be that easy...
  45. A

    Proving a 2:1 ratio triangle having a Zero Vector

    Homework Statement I need help once again with this question below: Thanks, aeromat The Attempt at a Solution This is what I have so far: GP = GQ + QP GQ = GP + PQ GR = GP + PR GP + GQ + GR = GQ + QP[-] + PQ[+] + GP + PR + GP GP + GQ + GR = GQ + 2GP + PR I am stuck...
  46. T

    Calculating the Amount of Type B Tea in a €12.65/kg Mixture

    Homework Statement Tea served in a canteen is made from a mixture of two different types of tea, type A and type B. Type A costs €12.15 per kg. Type B costs €12.90 per kg. The mixture costs €12.65 per kg. If the mixture contains 7kg of type A, how many kilograms of type B does it contain...
  47. B

    Calculating Single Gear Ratio

    Hi. I am designing a model for a vehicle. The power source is solar energy, providing power to a single 12 volt motor of about 1W. Through tests I have calculated the stall torque and max RPM of this motor, and therefore a rated torque of 0.00154 Nm. At this load the motor should ideally spin...
  48. T

    Need a little help with this ratio question

    Homework Statement A tank was 3/4 full of oil. 100 litres of oil were then used. If it was then 2/3 full, how many litres does the tank hold when full Homework Equations The Attempt at a Solution umm, I am not even sure how to get started, i know that 3/4 = 75% and 2/3 = 66.6%...
  49. P

    A question about Poisson's Ratio

    Does Poisson's Ratio only apply to material still in the linear elastic range or is it still true for the material that has undergone plastic deformation?
  50. 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...
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