Chapter 5. Calculator Modes

Non-decimal bases can be selected for display of numbers in the result and parsing of numbers in expressions. This include regular number bases (binary, octal, hexadecimal, sexagesimal) as well as sexagesimal time format and roman numerals. Other number bases, as well as base for expression input, can be selected from a dialog window accessed from Mode → Number Base → Other... or Mode → Number Base → Select Result and Expression Base....

The convert number bases dialog (see the section called “Convert Number Bases Dialog”) and the programming keypad (see Table 3.3, “Programming Keypad”) provides efficient conversion between common bases. For output of a single value to a specific number base use of the “to”-operator is recommended (see the section called “The “to” (and “where”) operators”). For input of single number in a specific base, the base() function, which in addition supports non-numerical bases, or base prefixes (“0b”, “0o”, “0d”, and “0x” for base 2, 8, 12, and 16, respectively) can be used.

These modes mainly control when numbers are displayed exponentially (e.g. “2.62E3” which equals “2620”). In the default normal mode, numbers are displayed in exponential format if the exponent will be greater than the current precision. In scientific mode the lowest exponent is 3. In simple numerical mode the exponential format is never used and it is always used in purely scientific mode. In the engineering mode, the exponent is always a multiple of three. This is naturally equivalently true for numbers less than one and negative exponents. When the scientific modes are selected in the keypad (not from the menubar), negative exponents are automatically activated and sort minus last deactivated, while normal and simple modes do the opposite.

If this option is on, Qalculate! will not round infinitely repeating digit sequences, if the digits in the sequence fits the maximum number of decimals. Instead “…” will be displayed after the repeated digits and the result indicated as exact (compare “9/11 ≈ 0,81818182” with “9/11 = 0,81 81…”).

By default approximately displayed numbers are rounded towards nearest decimal (e.g. “2.64 ≈ 2.6”, “2.67 ≈ 2.7”), and away from zero if the number is halfway between two values (e.g. “2.65 ≈ 2.7”, “−2.65 ≈ −2.7”). This can be changed by activating Round Halfway Numbers to Even (e.g. “2.55 ≈ 2.6”, “2.65 ≈ 2.6”) or Truncate Numbers (if activated, numbers are always rounded towards zero, e.g. “2.67 ≈ 2.6”).

If this option is on, approximate numbers in the result will be appended with zeroes, so that the number of digits (after preceding zeroes) will equal the precision.

If negative exponents is activated, division is shown as a negative power (e.g. “x × y^-1” instead of “x / y”).

This option decides if minus signs should be avoided in the first positions of the result expression.

Complex number can be displayed in rectangular/cartesian (e.g. “5i + 2”), exponential (e.g. “5.39 × e^1.19”), polar form (e.g. “5.39 × (cos(1.19) + i × sin(1.19))”), or angle/phasor notation (e.g. “5.39∠1.19”).

This controls if rational numbers are displayed as fractions or not. The exact decimal fraction mode displays the number as a simple fraction, if the rational number does not have an exact decimal representation which can be displayed using the number of digits allowed by the current precision. The rational number “4/3” is displayed as “1.3333333” (or “1.333…” if indicate repeating decimals is activated) in decimal fractions mode, as “4/3” in both exact decimal fractions and simple fractions mode, and as “1 + 1/3” in mixed fractions mode.

The automatic use of prefixes for units in results can be toggled on and off. By default prefixes are only used for a selection of units (mainly standard SI and CGS units), but this can be changed to also include currencies or all other units. By default prefixes representing a power of ten not dividable by three (centi, deci, deca and hecto), as well the new SI prefixes adopted in 2022 (ronna, quetta, ronto, and quecto), are not used automatically. If denominator prefixes are not explicitly enabled, prefixes will only be set for the numerator in a fractional unit expression (e.g. “1 Mg/m” or “1 kg/mm”), unless there is no unit in the numerator. Binary prefixes are never used automatically, unless activated for information units (bits, bytes, etc.) in the preferences dialog.

Units can be automatically converted to base units or the optimal units in results. Optimal conversion means that the number of units in the result is reduced to as few units as possible. Only SI units are used for conversion. If Convert to Optimal SI unit is activated, non-SI units are converted to SI units, even if equally or less optimal than the original unit(s). In optimal unit mode, currencies are converted to the local currency, unless deactivated in the preferences dialog. Mixed units conversion allows certain units, such as time units and many imperial/U.S. customary units, to be converted to a combination of appropriate units, e.g. “60.2 minutes = 1 hour to 12 seconds”.

The place units separately alternative controls the display of unit expressions in result. If it is enabled (default) units will be displayed separate from other parts of the expression at the end (compare “(5x × m)/(y × s)” and “5x/y m/s”).

The display of unit, prefix, variable and function names can be controlled by selecting to display abbreviations or full length names (e.g. “5 cm” or “5 centimeters”). Both abbreviations and long names can however always be entered in expressions.

When always exact mode is on, the calculation will not go further than what can be calculated exactly (e.g. “sqrt(2 + 3) = sqrt(5)”). The default “Try Exact” mode, will calculate the result exact as far as possible and then approximately. Approximate mode will directly calculate a approximate result, thus being a bit faster but giving a less correct approximate indication (“sin(pi/2)” return approximately one instead of exactly one). If the interval arithmetic mode is activated the precision of the final result is guaranteed by calculating an interval for every approximate value (See Chapter 6, Propagation of Uncertainty and Interval Arithmetic).

This controls the default assumptions for unknown variables without explicitly defined assumptions. See Chapter 7, Variables. The assume denominators non-zero alternative makes it possible to avoid the situation where expressions such as “(x-1)/(x-1)” can not be further simplified because the denominator might be zero (if x equals 1). With this alternative activated the example can be reduced to 1.

These options controls how expressions are interpreted. There are three main modes, which mainly controls if implicit multiplication is handled differently from explicit multiplication and if spaces are taken into account or not. See the section called “Implicit Multiplication and Parsing Modes”. If the read precsion option is activated, decimal numbers are intrepeted as approximate with precision equal to the number of digits (e.g. “1.1 × 3.20 = 1.1±0.05 × 3.20±0.005 ≈ 3.5±0.2”).

Precision specifies the default number of significant digits displayed and determines the precision used for approximate calculations. The internal precision is higher than the one specified, but will nevertheless not completely protect against loss of significance/catastrophic cancellation (and you will not be alterted unless interval arithmetic is activated).

In the decimals dialog, the number of decimals displayed can be controlled. This includes minimal (will fill out with zeroes) and maximal number of decimals (will round numbers).