# Get the correct answer quickly!

With its ergonomic keyboard and displays, its ability to handle arbitrary combinations of units, and its seamless integration of real and imaginary numbers, the Numerari scientific calculator app sets new standards for ease of use, unit conversion, and complex number support. Designed for the iPad and iPad mini, the keyboard puts keys within easy reach and includes user-defined keys that you can customize with a simple drag and drop. With Numerari's popup unit keypads, you can assemble any arbitrary combination of units and convert them to any other consistent set of units---there are no limitations on what physical quantities can be converted. Units and constants can also be included in any of your calculations so that Numerari can check for unit consistency and even suggest appropriate units for the answer! The complex number capabilities are just as comprehensive. Any combination of rectangular or polar forms can be included in calculations, and the final answer can be instantly toggled between rectangular or polar form and between radians or degrees using our "last answer" keys.

Calculations Are Clearly Formatted—The displays clearly format your calculations in two dimensions with practically textbook quality. When entering calculations, Numerari is unique in its ability to combine the ease of algebraic entry with the clear two-dimensional formatting so there is never any doubt about your expression's structure.

It's Easy to Add Units and Constants to Calculations and to Convert Units—If you want to add units and constants to your calculations, Numerari's special keypads let you include them quickly and routinely. Numerari can then check your calculations for unit consistency.

One Tap Copies an Answer or Expression from Your Calculation History—Every part of a displayed expression is touch sensitive. It has never been easier to reuse results and expressions from previous calculations.

User-Defined Keys Reduce Key Taps—Anything you can copy by tapping can be saved to a user-defined key with a simple drag and drop.

Advanced Functions Support a Wide Range of Applications—The functions used most often in math, science, and engineering are built in and can be entered with just one or two taps.

Complex Numbers Without the Complexity—Seamlessly mix rectangular and polar forms in calculations and use dedicated keys to format and analyze complex number answers.

Archive History Images for Reference, Documents, and Sharing—Generate an image of your calculation history that you can email or view full-screen for screen capture.

Lots of Number Formatting Options If You Want Them—The default number formatting mode may be all you ever need but there is also scientific and engineering notation and many ways to customize the modes.

Finally, there is built-in help to get you started quickly, and a variety of color themes to let you customize your Numerari.

### Calculations Are Clearly Formatted

Correctness starts with clarity. As you enter a calculation, Numerari formats it so that the structure of your calculation is always clear. Powerful cursor controls and undo/redo keys make it simple to edit and to recover from mistakes.

### It's Easy to Add Units and Constants to Calculations and to Convert Units

Numerari is the first calculator—app or handheld—that makes using units and constants so easy that they can be a routine part of your calculations. Adding units and constants to your calculations allows Numerari to check for unit consistency and catch possible errors. To add units and constants, there is no searching through deep menu hierarchies or trying to type names on a calculator keyboard. Numerari uses simple popup keypads that make all the common units and constants just one or two key taps away. You can also add metric prefixes and create arbitrary combinations of units. When you create a combination of units, Numerari lets you copy those units somewhere else with just a tap. If you will need that unit combination in the future, you can save it to a user-defined key. All this capability also makes Numerari a great unit converter.

Metric Units Keypad—meter, kilometer, angstrom, barn, hectare, liter, cubic centimeter, kilogram, gram, metric ton, atomic mass unit, second, minute, hour, day, hertz, angular hertz, newton, pascal, bar, ampere, volt, ohm, siemens, farad, henry, watt, coulomb, tesla, weber, joule, electron Volt, kilowatt-hour, radian, steradian, angular degree, angular minute, angular second, revolution, kelvin, degree Celsius, candela, lumen, lux, mole, katal, becquerel, gray, sievert

English Units Keypad—inch, foot, yard, mile, nautical mile, mil, light-year, international acre, knot, fluid ounce, cup, pint, quart, gallon, imperial gallon, barrel, teaspoon, tablespoon, ounce, troy ounce, pound, slug, short ton, stone, grain, carat, pound force, poundal, dyne pounds per square inch, torr, atmosphere, erg, therm, calorie (thermochemical), calorie (international table), Calorie (food), Btu (thermochemical), Btu (international table), horsepower, horsepower (electric), degree Fahrenheit, degree Rankine, footcandle, curie, radiation absorbed dose (RAD), roentgen, rem

Constants Keypad—speed of light, Avogadro constant, Planck constant, Boltzmann constant, Stefan Boltzmann constant, astronomical unit, gravitational constant, elementary charge, molar gas constant, permittivity of vacuum, permeability of vacuum,\ standard acceleration of gravity, characteristic impedance of vacuum, Faraday constant, Planck constant (h-bar), Rydberg constant, Bohr radius, Hartree energy, Bohr magneton, nuclear magneton, classical electron radius, proton gyromagnetic ratio, magnetic flux quantum, conductance quantum, molar volume of ideal gas (at 1 bar), molar volume of ideal gas (at 1 atm), Josephson constant, conventional Josephson constant, von Klitzing constant, conventional von Klitzing constant, first radiation constant, second radiation constant, fine structure constant, Euler's number, Euler-Mascheroni constant, golden ratio, electron mass, proton mass, neutron mass, muon mass, electron magnetic moment, proton magnetic moment, neutron magnetic moment, muon magnetic moment, Compton wavelength, proton Compton wavelength, neutron Compton wavelength, muon Compton wavelength

### One Tap Copies an Answer or Expression from Your Calculation History

Few calculations are done in isolation. You often pull in earlier results and slightly change or correct previous calculations. Anything you see in the history or build displays can be copied to the current cursor location with just a tap. For example, tap a number in your calculation history to copy it to the expression you are building. Tap units to copy them to another place where they are needed. Our intelligent copying algorithm automatically selects logical blocks of content.

### User-Defined Keys Reduce Key Taps

Many calculators offer memory storage locations or variables to hold important values, but using this memory often requires sequences of key taps. For some systems, you need a good memory just to remember what was stored in which location. Numerari uses a simple but powerful approach with user-defined keys that show their content as their labels. With just a drag and drop, you can save any selectable part of an expression to a user-defined key, and then one tap of that key copies its content to the current cursor location.

### Advanced Functions Support a Wide Range of Applications

In addition to the fundamental scientific functions on the main keyboard, the advanced functions keypad adds 42 more for math, science, and engineering.

Advanced Functions Keypad—permutations, combinations, factorial, double factorial, logarithmic function with any base, gamma function, log gamma function, digamma function, Riemann zeta function, error function, complementary error function, Airy function Ai, Airy function Bi, derivative of the Airy function Ai, derivative of the Airy function Bi, lnp1, expm1, hyperbolic sine, inverse hyperbolic sine, hyperbolic cosine, inverse hyperbolic cosine, hyperbolic tangent, inverse hyperbolic tangent, hyperbolic cosecant, inverse hyperbolic cosecant, hyperbolic secant, inverse hyperbolic secant, hyperbolic cotangent, inverse hyperbolic cotangent, cosecant, inverse cosecant, secant, inverse secant, cotangent, inverse cotangent, Hermite polynomials, Legendre polynomials, associated Legendre polynomials, Laguerre polynomials, associated Laguerre polynomials, Chebyshev polynomials (first and second kind), Bessel functions (first and second kind), Modified Bessel functions (first and second kind) spherical Bessel functions (first and second kind)

### Complex Numbers Without the Complexity

Complex numbers are fully integrated into Numerari's capabilities. You can easily enter complex numbers in rectangular or polar form, you can put units on complex numbers just like any other number, and you can tap a complex number to copy it and its units to the cursor. Dedicated keys select the default answer form (rectangular or polar) and the default angle measure (radians or degrees). The "last answer" keys let you quickly see a complex number in alternative forms.

### Archive History Images for Reference, Documents, and Sharing

You can generate images of your calculation history with a variety of options. Crop your history by specifying how many of your calculations should be included and set the background color to the normal calculator color, to white, or to transparent (for mixing with other graphics). You can specify left or right alignment of your calculations, you can turn dividing lines on or off, and you can even turn off the display of unit conversion specifications to give your calculations a more standard appearance. The images can be emailed or viewed full-screen so they can be saved with a screen capture.

### Lots of Number Formatting Options If You Want Them

The default number formatting mode has special features that make it very useable and perhaps the only mode you will ever need. If your answer is turning into just a string of insignificant leading zeros, the default mode automatically shows you more fractional digits. If a number gets too large or too small, the default mode switches to scientific notation (or engineering notation if you prefer). You may never want to change the settings, but if you are particular about number formatting, many options are available.

### Help Examples Show You the Fine Points

Although most features are obvious from looking at the keyboard, the built-in help has examples and discussions that fill in details and show you how to get the most out of Numerari. Each help example has a contract button that you can tap to move the help to the top of the screen as shown below. Tap the button again to expand the help.

# Help Supplement

The help key in Numerari displays examples for getting started along with discussions of some important details. It is probably best to review that information first. This section supplements the help with answers to additional questions.

### How do you pronounce Numerari and what does it mean?

We pronounce it "New-mer-are-ee" and it is a form of the Latin verb numerare meaning "to count" or "number". Since counting is the foundation of calculating, we thought it would a make a good name for a new kind of calculator app.

### What is the maximum number of expressions that can appear in the history display?

The history display saves up to 35 expressions. This conserves memory and keeps response time fast. If you want an old expression to stay in the history display, you can always tap the delete button on the left side of more recent history expressions to remove them and prevent the old expression from being pushed out of the history. Another way of preserving an expression or answer would be to save it to a user-defined key. Note that any size expression or answer can be saved to a user-defined key.

### Can I turn the keyboard click on and off?

Open the iPad Settings app (not the settings inside of Numerari). Depending on your iOS version, the "Sounds" category will be visible at the top level or you may have to tap the "General" category first to see the "Sounds" category. In either case, when you tap "Sounds", you should see a switch called "Keyboard Clicks" that controls whether or not you want keyboards to make a clicking sound in your various iPad apps. Numerari follows this setting to turn its click sounds on or off. Depending on your iOS version, you may have to restart an app for changes in this setting to take effect.

### Can I leave the constant and unit keypads up while I work?

You do not have to show and then hide these keypads every time you put in a constant or unit. If you want to, you can show them all the time and only hide them when you need to check the history.

### Can I do calculations without using units?

Yes, you can take advantage of Numerari's ease of use, touchable history, user-defined keys, complex numbers, and many other features without using units. If you are not working with units but you still want to use our predefined constants, you should turn off the "Constants Include Units" switch in the settings. Normally, one of our constants represents a number along with its units and if the surrounding expression does not have units, Numerari might complain about the units being inconsistent. Turning the "Constants Include Units" switch off in the settings means that a constant will simply represent a number without any units.

### How does Numerari determine the units on my answer?

Note first that you can always specify the units you want on your answer by ending your expression with the convert key and specifying the desired units. In this case, Numerari will check to make sure that the units you specified are consistent with the units of the expression and will then apply the proper scale factor to express the answer in those units. If you do not specify the units, Numerari internally simplifies the units in your expression and then attempts to choose reasonable units for the answer. Its goal is to use answer units that are as simple as possible, and it is often able to recognize when a single unit, such as J (joule) for energy or Pa (pascal) for pressure, is appropriate. However, there are cases when it is impossible for Numerari to always choose the desired units for the answer. For example, energy is usually specified in J (joule) and torque is usually specified in N-m (newton-meter). Unfortunately, both of these have the same dimensions and it is not possible to examine the expression and tell which of these the user wants on the answer. Since energy is much more common, Numerari chooses energy. If you were doing a lot of torque calculations, you could set up a user-defined key that specified a conversion to N-m and then just tap that key when you wanted the answer in units of N-m. The help in Numerari shows how to create user-defined keys.

### Why did I get a message about inconsistent units when I think my units are correct or I am not using units?

Are you using our predefined constants? If so, check the "Constants Include Units" switch in the settings. If you like to use units in your expressions, this switch should be turned on so that a predefined constant represents a number along with its units. If you do not like to use units in your expressions, this switch should be turned off so that a predefined constant just represents a number.

### What is the difference between CLR and CLR ALL?

CLR clears the build display but it can be undone if you change your mind. CLR ALL clears the build and history displays and cannot be undone. Note that CLR ALL does not clear the user-defined keys. To clear a user-defined key, touch and hold the key for several seconds until it clears.

### How does Numerari determine the matching of parentheses?

Numerari uses an algorithm for matching parentheses that is more sophisticated than algorithms you might be familiar with from other software. Once a parenthesis finds a match, the two parentheses "lock" together and are treated as a matching pair (unless, of course, one of them is deleted). This is important for supporting the two-dimensional formatting of expressions. With a more primitive algorithm, entering a new parenthesis could suddenly cause a distant parenthesis to be unmatched and this could result in a disturbing "jerking" of the two-dimensional expression formatting. With our algorithm, the overall structure of the expression is more stable. When you enter a new parenthesis in the middle of an expression in which all parentheses are currently matched, the new parenthesis will not match one of the current parentheses—they are all locked into matching pairs. Instead, the new parenthesis will remain unmatched until you enter a matching parenthesis for it. Note that an unmatched parenthesis has a reddish color instead of black.

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