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. J

    Engineering Calculating Poisson's Ratio: Young, Bulk, & Relation

    I've never really heard of Young, Bulk, or Poisson's ratio before. I have done some research but I can't seem to find the relationship between the three in order to calculate Poisson's ratio. Could someone please point me in the right direction? Thanks
  2. e101101

    Rayleigh Scattering: Blue/Red Irradiance Ratio & Distance

    Hi everyone, does the scattering irradiance ratio between blue/red change with distance with Rayleigh scattering? I would think that it would remain generally constant..
  3. M

    I Exploring the Golden Ratio in Hexadecimal: How to Calculate the First 50 Digits

    I am not sure if this is the right section for this, but i didn't find it anywhere and I really need it. Can someone point me towards a place/tell me a program where I can get/compute the first (at least) 50 digits in the hexadecimal representation of the golden ratio? Thank you!
  4. posto002

    What is the ratio of the distances traveled by these two players?

    I couldn't really understand how to approach this problem with just given the inertia with Pierre have a mass of 70% less than Jean-Claude. As I understand it, because Jean-Claude is heavier, he must not have traveled as far as Pierre, but I am unable to find exactly how far each of them went...
  5. W

    Symmetric top with constant charge to mass ratio in a magnetic field

    Setup: Let ##\hat{\mathbf{e}}_1,\hat{\mathbf{e}}_2,\hat{\mathbf{e}}_3## be the basis of the fixed frame and ##\hat{\mathbf{e}}'_1,\hat{\mathbf{e}}'_2,\hat{\mathbf{e}}'_3## be the basis of the body frame. Furthermore, let ##\phi## be the angle of rotation about the ##\hat{\mathbf{e}}_3## axis...
  6. E

    B How to tell if a quantity is defined as a derivative or a ratio

    I appreciate that this is perhaps a strange question but it's been bugging me a little. For instance, velocity is defined as the time derivative of position, so will always appear as the gradient a graph of x vs t. However, something like resistance as R = V/I is defined in terms of a ratio...
  7. H

    Did I find the correct ratio in this magnetic field question?

    I used the two equations i listed by using B1=B2 and by doing that i ended up finding that N1/N2=λ. However i am not sure if that's the correct answer as λ is just a variable and not an actual number. Do you think it has to be an actual number or is it not really necessary?
  8. vchi

    Engineering Need to find L/D ratio for F117

    I was trying to look for an L/D ratio published everywhere on the web and I can't seem to find it for our project. Since I couldn't find it, I wanted to try calculating myself. Can't seem to find $$C_l$$ or $$C_d$$ though without some sort of paywall on research papers. So L/D would just be...
  9. R

    Calculate the gear ratio for every gear

    Hi, I have Force vs velocity graph. From the graph, I need to calculate the gear ratio of every Gear. This is the formula what I can use to find the gear ratio, V= 2*pi*r.n(1-i)/ε v= vehicle speed m/s ( I consider from the graph lowest speed 3.61 m/s or 13km/h r= radius of drive wheel...
  10. M

    Chemistry What is the ratio of pH=Pka-1?

    I think it is 1:10 but I am not sure the meaning of PKa -1, can someone explain it please.
  11. D

    Double slit: ratio of intensity of 3rd- and 0th-order maxima

    Homework Statement: In a double slit experiment let d=5.00 D=30.0λ. Estimate the ratio of the intensity of the third order maximum with that of the zero-order maximum. Homework Equations: interference diffraction i guess the goal is this equation ##I_{(\theta)}=I_0 \times(cos^2\beta)\times...
  12. karush

    MHB 71 Under what conditions does the ratio A}/B equal A_x//B_x

    71.15 Two vectors $\vec{A}$ and $\vec{B}$ lie in xy plane. Under what conditions does the ratio $\vec{A}/\vec{B}$ equal $\vec{A_x}/\vec{B_x}$? Sorry but I had a hard time envisioning what this would be? also thot I posted this earlier but I can't find it
  13. Manasan3010

    Understanding Velocity Ratios: Derivation and Confusion Explained

    I was able to derive, ##1/2*1*v_1^2 = 1/2*4*v_2^2 \\ v_1=2v_2 ## But I am confused whether the ratio is 1:2(Looking at the coefficient) or 2:1
  14. V

    Moisture Ratio in Air: Why Do Tables Stop at 50°C?

    Wondering why moisture ratio tables related to temperature and air only go up to roughly 50 C or so? is that temperature a "boundary" on the amount of water air can hold?
  15. G

    AB YOUR ANSWER: "Understanding the Ratio Detector Circuit: Explanation and Tips

    Hi, I built the attached ratio detector circuit and it works but I can't understand the reason for the connection marked in green. I need an explanation, please. Thanks in advance. GR
  16. K

    B Understanding Ratio Basics: A Guide to Splitting Costs with a 3:1 Ratio

    A friend of mine said he would share the price with me by 3:1 ratio. I have left school for many years. I'd like to know, what does it mean? For example, he gets 3 and I get 1, and the price is $1000, how much will I get? Will I get 1000 x 1/3 or 1000 x 1/4
  17. T

    Ratio of total refelected intensity compared to incident intensity

    Diagram Calculations as follows $$\frac{I_{total \: Reflection}}{I_{Incident}}=\frac{I_{R_1}+I_{R_2}}{I_0}*100=\frac{R*I_0+(R*T)*I_0}{I_0}$$ Subbing in the relevant equations given in the question $$\frac{I_{total \...
  18. Kaushik

    The ratio of compression of springs from three different setups

    I got the compression for the first one. Second one, i am a bit confused. But i got ## x_2 = \frac{F}{2k} ## In the third one, what will the compression be? I have to get the ratio ## x_2 : x_3 ## . Then i will be able to get my answer. Thanks.
  19. E

    How do I select the right motor and gear ratio for a mid-drive e-Bike?

    Hey all! I am working on my first ebike build and posted a question about friction drives earlier. Now, I have decided to go with a Mid-drive. I made calculations and found out the torque and rpm required for the build. But I am having difficulty find the right motor and gear ratio. I am trying...
  20. Monoxdifly

    MHB [ASK] Find the ratio of the area of triangle BCH and triangle EHD

    A parallelogram ABCD has angle A = angle C = 45°. Circle K with the center C intercept the parallelogram through B and D. AD is extended so that it intercepts the circle at E and BE intercepts CD at H. The ratio of the area of triangle BCH and triangle EHD is ... Here I got that triangle BCH...
  21. M

    A Golden ratio fractal phase conjugation

    So, I recently heard about the Golden ratio fractal phase conjugation and I was wondering if it could possibly explain the solar system formation. Meaning, if you can imagine a torus energy dynamic shape (with the sun in the middle) maybe it could be explained by this theory?
  22. K

    I Understanding the W Decay Branching Ratio to Quarks & Gluons

    Hello! In Modern Particle Physics by Mark Thomson, in the Electroweak Unification chapter, pg. 412 he talks about the branching ration of the W decay to quarks. And for this he includes both the ##W\to q \bar{q'}## and ##W\to q \bar{q'}g## i.e. the state with a gluon and 2 quarks in the final...
  23. Z

    Turns ratio of an Armstrong oscillator

    The result of my calculation doesn't seem right for me. Can you please help me find where did I go wrong with it. Thank you!
  24. A

    MHB What is the Range of a/b When ln(a+1)/ln(b+1) = x?

    Hi, I am working on a data set and I have log-transformed two variables a and b and would like to figure out the relationship between the respective ratios. I have a strong intuition that a/b should have a well-defined range for a given value of lna/lnb, but my maths is poor. a and be are...
  25. K

    Calculate the concentration ratio

    Any hint? I was immediately thinking standard electrode potentials as we have two half reactions, but not sure exactly how to go on..
  26. E

    Surface area to volume ratio

    In a human body we have two relatively similar structures -pulmonary...
  27. PCal

    Calculate the actual fuel:air ratio by volume and by mass

    By Volume: Butane 0.75x6.5= 4.875 moles of O2 Propane 0.1x5= 0.5 moles of O2 Butene 0.15x6= 0.9 moles of O2 Total O2 4.875+0.5+9= 6.275 moles Air required 6.275/0.21=29.88 moles/m^3 With 10% excess air 29.88x1.1= 32.868moles 1 mole fuel:32.87 moles of air By Mass: CO2 Moles...
  28. C

    Automotive Front Wheel Drive or Rear Wheel Drive has higher maximum slip ratio?

    The graph is relationship between longitudinal force and slip ratio under the conditions of 0 longitudinal acceleration and flat road(0 angle of inclination). Which line represent FWD or RWD? Does FWD or RWD have higher maximum slip ratio?
  29. caters

    Are my calculations of the pregnancy ratio of the population correct?

    Monthly Cycle numbers Here is the cycle ratio: $$2_{early}:2_{fertile}:1_{late}$$ And the numbers: $$20,000_{early}:20,000_{fertile}:10,000_{late}$$ Now, let's divide the early into 2 groups, pre-fertile, and safe and assume there is a 50/50 split between those 2 groups. Let's also assume...
  30. I

    Ratio of Intensities of 2 sounds

    Homework Statement The decibel scale of loudness is L = 10 log##\frac{I}{Io}## where I, measured in watts per square meter, is the intensity of the sound and Io= ##10^-12## watt/m 2 is the softest audible sound at 1000 hertz. Classical music typically ranges from 30 to 100 decibels. The human...
  31. J

    MHB Ratio word problem: What fraction of the original counters remain in the bag

    I have a word equation i cannot figure out! anyone have any ideas? There is a large bag of red and blue counters. One red and one blue counter are removed from the bag. This process is repeated until 1/4 of the red counter and 3/5 of the blue counters have been removed. What fraction of the...
  32. L

    Gears create more torque? Prove it

    Hi guys, I was sizing up a servo motor the other day and started thinking. While we all know gear ratios will effectively "convert" speed into torque. I couldn't help wondering about the initial starting conditions.. The problem below... Lets say I have a motor with a max load of 1Kg...
  33. chwala

    Find the area of the shaded region as a ratio to the area of the square

    Homework Statement find the area of the shaded region as a ratio to the area of the square (kindly see attached diagram)Homework EquationsThe Attempt at a Solution ##A= \frac 1 2####b×h## ##A= \frac 1 2####×2x × 3x##
  34. Othman0111

    Python How to increase the acceptance ratio

    I trying to generate a random distribution λe-λy Which distributed exponentially.%matplotlib inline import numpy as np from matplotlib import pyplot N = 1000 r = np.random.random(N) xlambda = 0.1 x = -np.log(r)/xlambda binwidth=xlambda*5 pyplot.hist(x,bins=np.arange(0.,100...
  35. MathematicalPhysicist

    I A question regarding the ratio test for limits

    So we have the theorem: if ##a_n>0## and ##\lim_{n\to \infty} a_{n+1}/a_n = L## then ##\lim_{n\to \infty} a_n^{1/n}=L##. Now, the proof that I had seen for ##L\ne0## that we choose ##\epsilon<L##. But what about the case of ##\epsilon>L##, in which case we have: ##a_{n+1}>(L-\epsilon)a_n## but...
  36. Z

    Calculating gear ratio from the motor's graph for an EV?

    Dear community, For my electric vehicle project I want to select a gear ratio (single) of my gear box and send this information to the supplier. In order to calculate this ratio I thought of the following steps but am not sure and want some expert to recheck and answer my queries: 1. Calculate...
  37. Cerenkov

    B Ratio between the sizes of the Observed and the Entire Universe

    Hello. I have some questions regarding Alan Guth's book on the Inflationary Universe. The following, from pages 185 & 186, has piqued my interest. I have reproduced Figure 10.6, above. Please read on. My questions follow. Please also take note that I can only understand these matters at a...
  38. mec_divi

    Aspect ratio for a motorcycle tire

    can anyone tell me the method by which the aspect ratio for the motorcycle tire can be decided given that load capacity of bike is known.
  39. Cerenkov

    B Ratio of Earth-Sized exoplanets to other sizes of exoplanet?

    Hello. In this issue of the American Scientist magazine, https://www.americanscientist.org/magazine/issues/2018/september-october, there's an article by Dominik Kraus of the Helmholtz-Zentrum Dresden-Rossendorf Institute of Radiation Physics about the internal composition of the planets Uranus...
  40. Krushnaraj Pandya

    Ratio of the length of resistive wires in a square

    Homework Statement In a given square ABCD each side is of 1 m and resistance of wire is 1 ohm/m. A resistance of 1 m is connected from A to E (which lies on side CD). A constant potential difference is applied across A and C, if potentials of B and E are same then find CE/ED. Homework...
  41. G

    Ratio of the Electric field to the Magnetic field

    Dear all. I would like to know the general expression of the ratio of the electric field strength E to the magnetic flux density B. I know E/B = c, where c is the speed of light, for a vacuum, but I want to know if this is stil valid for any material where the electric and magnetic fields are...
  42. M

    FM Ratio Detector is not working

    hi , please can somebody help me about this circuit, is not working i don't get audio signal here is my circuit rename in asc frm txt thanks
  43. C

    Velocity Ratio in Gears & Wheels Systems: Inverting?

    Hi, if the velocity ratio is equal to the distance traveled by the effort divided by the distance traveled by the load, in a gears and wheels system, do you invert that in the case or gears? Making it number of teeth on driven gear divided by number of teeth on driving gear? Thanks
  44. T

    What Is the Correct Way to Calculate Poisson's Ratio?

    Hello all I was hoping someone could help clarify Poissons ratio. I understand that it is Lateral Strain / Axial Strain but I wanted to understand it in the context of an example. The question is:- At 5kN compression load Original Depth = 30mm Change in Depth = 2mm Original Height = 100mm...
  45. J

    MHB Ratio of Chen and Father's age: How old is Miss Chen's father now?

    The ratio of Miss Chen's age to her father's age is 2:5. In 8 years' time, the ratio of their ages will become 1:2. How old is Miss Chen's father now? My work. Age of Chen = C Age of Father = F ----------------------------------------------------------------------------------------- Method 1...
  46. Dukon

    What motor/payload mass ratio -> payload spins the motor

    Given an unconstrained (suspended without contact to anything) electric motor with its own power in total has mass m1 Given the motor shaft is connected to a payload of mass m2 If m1>m2 then: m1 no-spin + m2 spin If m2>m1 then: m1 spin + m2 no-spin What happens at the unit ratio (m1/m2 = 1...
  47. S

    Fraunhofer Diffraction Pattern Ratio of Power Densities

    Homework Statement Find an approximate expression for the ratio of the power densities at the principal maximum to that at the first secondary maximum on either side, in the Fraunhofer diffraction pattern of an N-slit multiple aperture. Assume that the slits are much narrower than their...
  48. S

    Calculating the Ratio of Apparent Weight on a Ferris Wheel

    Homework Statement A Ferris wheel 26 m in diameter rotates once every 14 s. What is the ratio of a person's apparent weight at the top of the ride to her apparent weight at the bottom of the ride? Homework Equations [/B] FNT/FNB = mg - mv^2 / r / mg + mv^2/r The Attempt at a Solution...
  49. vAhmed

    Calculating a ratio in Free Fall motion

    Homework Statement A ball is thrown upward with a speed v 1. The ball reaches a maximum height of y=h. What is the ratio of the speed of the ball,v 2 , at y=h/2, to the initial upward speed of the ball,v 1 , at y=0? Homework Equations I attached a picture. We are currently studying the four...
  50. N

    A What is the dust-to-gas ratio in oxygen-poor galaxies?

    Hello, Assuming that dust is formed by silicates with Mg and Fe. What is the largest possible silicate dust-to-gas ratio in mass?
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