# What is Floating: Definition and 271 Discussions

In computing, floating-point arithmetic (FP) is arithmetic using formulaic representation of real numbers as an approximation to support a trade-off between range and precision. For this reason, floating-point computation is often used in systems with very small and very large real numbers that require fast processing times. In general, a floating-point number is represented approximately with a fixed number of significant digits (the significand) and scaled using an exponent in some fixed base; the base for the scaling is normally two, ten, or sixteen. A number that can be represented exactly is of the following form:

significand

×

base

exponent

,

{\displaystyle {\text{significand}}\times {\text{base}}^{\text{exponent}},}
where significand is an integer, base is an integer greater than or equal to two, and exponent is also an integer.
For example:

1.2345
=

12345

significand

×

10

base

4

exponent

.

{\displaystyle 1.2345=\underbrace {12345} _{\text{significand}}\times \underbrace {10} _{\text{base}}\!\!\!\!\!\!^{\overbrace {-4} ^{\text{exponent}}}.}
The term floating point refers to the fact that a number's radix point (decimal point, or, more commonly in computers, binary point) can "float"; that is, it can be placed anywhere relative to the significant digits of the number. This position is indicated as the exponent component, and thus the floating-point representation can be thought of as a kind of scientific notation.
A floating-point system can be used to represent, with a fixed number of digits, numbers of different orders of magnitude: e.g. the distance between galaxies or the diameter of an atomic nucleus can be expressed with the same unit of length. The result of this dynamic range is that the numbers that can be represented are not uniformly spaced; the difference between two consecutive representable numbers varies with the chosen scale.

Over the years, a variety of floating-point representations have been used in computers. In 1985, the IEEE 754 Standard for Floating-Point Arithmetic was established, and since the 1990s, the most commonly encountered representations are those defined by the IEEE.
The speed of floating-point operations, commonly measured in terms of FLOPS, is an important characteristic of a computer system, especially for applications that involve intensive mathematical calculations.
A floating-point unit (FPU, colloquially a math coprocessor) is a part of a computer system specially designed to carry out operations on floating-point numbers.

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4. ### Comp Sci Converting Float to Char in C: Exploring the Use of sprintf

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5. ### Density versus Pressure -- Balancing the bouyancy of a floating capsule

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6. ### Engineering Hydrostatic Pressure of Ball Floating in Liquid

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9. ### B Free fall floating in a closed spaceship near a gravity source

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10. ### Calculate dimensions of floating laptop stand

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12. ### Floating a cruise ship in a bucket of water

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13. ### Why Are There Floating Point Errors When Parsing Data in Pandas?

I am parsing data from an excel sheet using pandas ExcelFile class and read_excel function. I noticed that when reading the file, there are floating point errors in the results. For example, a cell that contains 25.15 will be 25.149999999999977 in the pandas data frame. The value 25.15 in Excel...
14. ### Fortran Solving Magnetic Field Using Floating Random Walk

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16. E

### Stability of a floating cylinder

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17. ### Engineering Using the Archimedes Principle to do calculations for this floating buoy

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18. ### Comparing densities of three bodies floating to different depths

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19. ### Gauge pressure due to a floating body

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21. ### Calculating the Second Moment of Area for Floating Bodies

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23. ### How Does the Volume of a Block Affect Its Buoyant Force?

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24. ### Perfect Floating Ball Illusion (inspired by Jeff Koons' Art)

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I recall reading somewhere about when anything, (eg. cars on the road, balls in a flowing stream) tend to clump together on curves. I don't remember where I read it but I seem to think there was some principal involved. Has anyone ever heard of this before, or am I mistaken. Thanks.
26. ### Mechanical vibrations: floating apple

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29. ### Conductor sphere floating on a dielectric fluid

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30. ### Floating potential of a conductor in an electrical field

I'm interested in the following general question: Assume x,y,z is an axes system, and that the y-z plane is occupied by a conductive plate at a known potential V with respect to the earth. Now, a conductive material M of neutral global electrical charge is placed at some distance of the plate...
31. ### Can a Floating Voltage be Generated Without an Auxiliary Low Voltage Battery?

In this circuit i want generate the floatin voltage from the external supply connected by a load to drain of transistors (suppose this is constant). So for me is possible to command the gates without an auxiliary low voltage battery. Taking advantage of the high sensitivity of the mosfet I...
32. ### Use of 4 floating current sources

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34. ### Is free fall NOT the same as floating in space?

For many, many years (don't ask), I've been running into the classic example of the local reference frame: the man in the box who can't tell if he's floating free in space, or falling into a gravity well. It occurs to me that if one is in a falling box, a mass released at the top of the box...
35. ### Ball floating on the surface of water

Homework Statement Homework EquationsThe Attempt at a Solution When air is evacuated , atmospheric pressure pushing down the cork is eliminated , cork should rise a little i.e option b) . This is incorrect . What am I missing ?
36. ### Question about springs to support a "floating" table

I have been searching but I have not been able to find the information I am looking for. I want to build a "floating table" that is supported by one or more compression springs. When an object is added the table will lower by just a bit. As another object is stacked on top of the first one...
37. ### Testing floating point numbers for equality

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38. ### B Would it be possible to make something float?

While waiting in the doctor’s office, I looked at a balloon sticker on the wall. That made me think (once again). Would it be possible to make something float without using your basic flotation stuff (helium and propellers mostly)? I was thinking in more of a futuristic themed way. Like magnets...
39. ### Floating Water Bridge and Dielectric Strength per Volume

I recently watched a great video demonstrating the floating water bridge experiment: At around 34 sec, you can see an electrostatic discharge before the water bridge forms. I've read that this is due to the electrostatic breakdown of air between the two beakers.This made me curious about the...
40. ### Newbie question -- A train in space with a ball floating in a train car....

Hello, I am someone who has no experience in physics other than primary/high school and I have a quick simple question about something I can't wrap my mind around as a complete physics newbie. Please have understanding. The question: let's say a train is standing still at a point in space (so...
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42. ### Biconvex Lens Floating on Mercury

Homework Statement A thin bi-convex lens with refractive index n has spherical surfaces with equal radii of curvature r and measured focal length f. The lens floats horizontally on the surface of liquid mercury so that its lower surface effectively becomes a spherical mirror. A point object on...
43. ### Equilibrium Force on Floating Object

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44. ### Optimizing Mass for Vertical Rod Buoyancy in Unknown Fluid

Homework Statement A 0.75-m rod has a uniform linear mass density of λ. A small mass m with negligible volume is attached to one end of the rod. The rod with the attached mass is placed in a container of unknown ﬂuid and after oscillating brieﬂy, comes to rest at its equilibrium position. At...
45. ### B How to stop insulation from floating when flooded

Elsewhere someone is planning to install Under Floor Heating (UFH) in a house that is prone to flooding. UFH systems typically comprise a layer of insulation then a layer of concrete screed with UFH pipes in it. Given this recent news story...
46. ### Power Factor Correction (open leg on a floating wye)

We had a switch fail to close on the A phase of a floating wye connected capacitor bank. The C phase fuse was found to be bad and was replaced, however the B phase fuse then blew. The bad switch was then found and replaced. After that the system operated normally. The contractor said the...
47. ### Floating Launch Loop: Is It Worth Exploring? - roboticsolutions.tech

im writing a 2d space simulator and in it i want to simulate rockets as well as things like space elevators and spaceguns to allow players to compare how each system works and compare pros and cons. one idea i want to include in that simulator is my own that i want to promote to the new...
48. ### How does a ground loop and a floating ground work?

Hello Forum, In DC circuits, I understand that a ground is a point or an entire conductor where the electric potential is set to be V=0 and the potential V at any other point in the circuit is referenced to that. How does the the concept of ground loops work? Why are they not desirable? What...
49. ### B Upthrust & Floating: Confirm Position in Liquid

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50. ### Help me move a floating bridge 90 degrees w/o getting wet

Hello! I was hoping someone here could help me solve a real world problem. So my university pool has something called a bulkhead, which is basically a bridge that floats above the water so that people can walk across the shorter dimension of the rectangular pool (50 meters long, 25 yards wide)...