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# Significant figures

The significant figures (also known as the significant digits) of a number are digits that carry meaning contributing to its measurement resolution. [1]

## Absolute value

In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.

## Accuracy and precision

Precision is a description of random errors, a measure of statistical variability.

## Approximation error

The approximation error in some data is the discrepancy between an exact value and some approximation to it.

## Area of a circle

In geometry, the area enclosed by a circle of radius is.

## Base (exponentiation)

In exponentiation, the base is the number b in an expression of the form bn.

## Benford's law

Benford's law, also called Newcomb-Benford's law, law of anomalous numbers, and first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data.

## Binary number

In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one).

## Binomial proportion confidence interval

In statistics, a binomial proportion confidence interval is a confidence interval for the probability of success calculated from the outcome of a series of success–failure experiments (Bernoulli trials).

## Common logarithm

In mathematics, the common logarithm is the logarithm with base 10.

## Decimal

The decimal numeral system (also called base-ten positional numeral system, and occasionally called denary) is the standard system for denoting integer and non-integer numbers.

## Decimal separator

A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form.

## Engineering notation

Engineering notation or engineering form is a version of scientific notation in which the exponent of ten must be divisible by three (i.e., they are powers of a thousand, but written as, for example, 106 instead of 10002).

## Error bar

Error bars are graphical representations of the variability of data and used on graphs to indicate the error or uncertainty in a reported measurement.

## False precision

False precision (also called overprecision, fake precision, misplaced precision and spurious precision) occurs when numerical data are presented in a manner that implies better precision than is justified; since precision is a limit to accuracy, this often leads to overconfidence in the accuracy, named precision bias.

## Floating-point arithmetic

In computing, floating-point arithmetic is arithmetic using formulaic representation of real numbers as an approximation so as to support a trade-off between range and precision.

## Floor and ceiling functions

In mathematics and computer science, the floor function is the function that takes as input a real number x and gives as output the greatest integer less than or equal to x, denoted \operatorname(x).

## Hecto-

Hecto- (symbol: h) is a decimal unit prefix in the metric system denoting a factor of one hundred.

## IEEE 754

The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point computation established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE).

## Interval arithmetic

Interval arithmetic, interval mathematics, interval analysis, or interval computation, is a method developed by mathematicians since the 1950s and 1960s, as an approach to putting bounds on rounding errors and measurement errors in mathematical computation and thus developing numerical methods that yield reliable results.

## Kahan summation algorithm

In numerical analysis, the Kahan summation algorithm (also known as compensated summation) significantly reduces the numerical error in the total obtained by adding a sequence of finite precision floating point numbers, compared to the obvious approach.

## Kinetic energy

In physics, the kinetic energy of an object is the energy that it possesses due to its motion.

A leading zero is any 0 digit that comes before the first nonzero digit in a number string in positional notation.

## Logarithm

In mathematics, the logarithm is the inverse function to exponentiation.

## Normalized number

In applied mathematics, a number is normalized when it is written in scientific notation with one non-zero decimal digit before the decimal point.

## Numerical digit

A numerical digit is a single symbol (such as "2" or "5") used alone, or in combinations (such as "25"), to represent numbers (such as the number 25) according to some positional numeral systems.

## Order of magnitude

An order of magnitude is an approximate measure of the number of digits that a number has in the commonly-used base-ten number system.

## Overline

An overline, overscore, or overbar, is a typographical feature of a horizontal line drawn immediately above the text.

## Plus-minus sign

The plus-minus sign (±) is a mathematical symbol with multiple meanings.

## Positional notation

Positional notation or place-value notation is a method of representing or encoding numbers.

## Precision (computer science)

In computer science, the precision of a numerical quantity is a measure of the detail in which the quantity is expressed.

## Propagation of uncertainty

In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them.

## Round-off error

A round-off error, also called rounding error, is the difference between the calculated approximation of a number and its exact mathematical value due to rounding.

## Rounding

Rounding a numerical value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example, replacing \$ with \$, or the fraction 312/937 with 1/3, or the expression with.

## Scientific notation

Scientific notation (also referred to as scientific form or standard index form, or standard form in the UK) is a way of expressing numbers that are too big or too small to be conveniently written in decimal form.

## Significance arithmetic

Significance arithmetic is a set of rules (sometimes called significant figure rules) for approximating the propagation of uncertainty in scientific or statistical calculations.

## Significand

The significand (also mantissa or coefficient) is part of a number in scientific notation or a floating-point number, consisting of its significant digits.

## Trailing zero

In mathematics, trailing zeros are a sequence of 0 in the decimal representation (or more generally, in any positional representation) of a number, after which no other digits follow.

## Underline

An underline, also called an underscore, is a more or less horizontal line immediately below a portion of writing.

## Unit of measurement

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

## Unit prefix

A unit prefix is a specifier or mnemonic that is prepended to units of measurement to indicate multiples or fractions of the units.

## Vinculum (symbol)

A vinculum is a horizontal line used in mathematical notation for a specific purpose.

## References

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