Unit of Measure Conversions

Definitions

Arithmetic Mean
The arithmetic mean - or average - of n numbers a,b,c,... is the sum of their values divided by the number of values: (∑a,b,c,...)/n

Example: The arithmetic mean of 1,2,2,3,4,6,7,9 is: (1+2+2+3+4+6+7+9)/8 = 34/8 = 4.25

Baker's dozen
13
Brace
2
Complex Numbers
Numbers having both a real number component and an imaginary number component: (a+bi)

Example: (3+5i)

Defective Numbers
Positive integers, each of whose divisors add up to less than the number itself.

Example: 10 has divisors 1,2,5 that sum to 8

Dozen
12
Excessive Numbers
Positive integers, each of whose divisors add up to more than the number itself.

Example: 12 has divisors 1,2,3,4,6 that sum to 16

Factorial
The factorial of a positive integer n is the product of all positive integers that are equal to or less than n:
n! = ∏(n,n-1,n-2,...,3,2,1)

Example: Factorial 5 is: 5! = 5x4x3x2x1 = 120

Geometric Mean
The geometric mean of n positive numbers a,b,c,... is the nth root of the product of their values:
n√(∏a,b,c,...)

Example: The geometric mean of 1,2,2,3,4,6,7,9 is: 8√(1x2x2x3x4x6x7x9) = 8√18144 = 3.41

Gross
144
HCF - Highest Common Factor
The highest common factor (or greatest common divisor - GCD) for two or more positive integers is the largest positive integer that divides exactly into all of them.

Example: The highest common factor of 24,60,96 is: HCF(24,60,96) = 12

Imaginary Numbers
Numbers usually expressed as real numbers multiplied by the square root of -1 (i).

Example: 2i, such that (2i)2 = -4

Irrational Numbers
Numbers that cannot be expressed either as a whole number or as a fraction.

Examples: √2 [= 1.41421356...]; π [= 4(1/1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 - 1/15 ...)]

LCM - Lowest Common Multiple
The lowest (or least) common multiple for two or more positive integers is the smallest positive integer that is exactly divisible by all of them.

Example: The lowest common multiple of 3,4,8 is: LCM(3,4,8) = 24

Median
The median is the middle number in a group of numbers arranged in ascending order. If there is an even number of values in the group, the median is the average of the two middle numbers.

Example: The median of 1,2,2,3,4,6,7,9 is: (3+4)/2 = 3.5

Mode
The mode of a group of numbers is the number that appears most often. If two or more values are repeated the same number of times, the group is said to be bimodal or multimodal.

Example: The mode of 1,2,2,3,4,6,7,9 is: 2

Natural Numbers
The set of monotonically increasing positive integers, starting with 1, that are used for counting and ordering.
NTP - Normal Temperature and Pressure - current definition
Temperature: 20°C (68°F / 293.15 K)
Pressure: 101.325 kPa (1 atm / 29.921 in-Hg / 14.6959 psi / 760 torr)

Source: NIST (National Institute of Standards and Technology, USA)

NTP - alternate definition
Temperature: 20°C (68°F / 293.15 K)
Pressure: 101.3 kPa (1 atm / 29.9 in-Hg / 14.69 psi / 760 torr)

Source: ISO-5011 (International Organisation for Standardisation) at 50% Relative Humidity (RH)

Perfect Numbers
Positive integers, each of whose divisors add up exactly to the number itself.

Example: 6 has divisors 1,2,3 that sum to 6

Rational Numbers
Whole numbers and fractions.

Examples: 5; ⅔

Real Numbers
The union of both rational and irrational numbers.
Score
20
STP - Standard Temperature and Pressure - current definition
Temperature: 0°C (32°F / 273.15 K)
Pressure: 100 kPa (1 bar / 29.53 in-Hg / 14.5038 psi / 750.06 torr)

Source: IUPAC (International Union of Pure and Applied Chemistry) since 1982

STP - alternate definitions
Temperature: 0°C (32°F / 273.15 K)
Pressure: 101.325 kPa (1 atm / 29.921 in-Hg / 14.6959 psi / 760 torr)

Sources: ISO-10780; IUPAC until 1982; NIST

Temperature: 15°C (59°F / 288.15 K)
Pressure: 101.325 kPa (1 atm / 29.921 in-Hg / 14.6959 psi / 760 torr)

Source: ISO-13443 at 0% RH

Temperature: 15°C (59°F / 288.15 K)
Pressure: 101.33 kPa (1 atm / 29.92 in-Hg / 14.696 psi / 760 torr)

Sources: ISO-2314 at 60% RH; ISO-3977-2 at 60% RH

Whole Numbers
The set of monotonically decreasing negative integers, starting with -1, combined with zero and natural numbers.

Hints and Tips

BODMAS
A memory aid that defines the order of evaluation of an expression. This is generally from left to right, taking into account the following order of precedence:
  1. Brackets first,
  2. Orders (powers and roots) next,
  3. Division and
  4. Multiplication next, then
  5. Addition and
  6. Subtraction last.
Division and Multiplication rank equally, so are simply evaluated from left to right.
Addition and Subtraction also rank equally, so are also evaluated from left to right.

It is recalled to mind as "Boys Only Do Maths And Science".

ROYGBIV
A memory aid that defines the order of colours in the visible light spectrum:
  • Red
  • Orange
  • Yellow
  • Green
  • Blue
  • Indigo
  • Violet

It is recalled as "Richard Of York Gave Battle In Vain".

SOH-CAH-TOA
A memory aid for calculating the Sine, Cosine and Tangent of an acute angle in a right-angled triangle:
  • Sin = Opposite / Hypotenuse
  • Cos = Adjacent / Hypotenuse
  • Tan = Opposite / Adjacent

It is recalled as "Old Horses Always Have Old Actions".

√2
"I want a root of two!" is a memory aid to recall the square root of two.
The lengths of the first five words in the phrase yield 1.4142.
√3
"O provide for me a root of three!" is a memory aid to recall the square root of three.
The lengths of the first five words in the phrase yield 1.7321.
3
To determine if a number is exactly divisible by three, add all its digits together.
If this sum is exactly divisible by three then so is the original number.
5
To multiply a number by five: append a trailing zero and halve the result.
To divide a number by five: double the number, then shift the decimal point one place to the left.
11
To determine if a number is exactly divisible by eleven: add all its even-position digits together and subtract the result from the sum of all its odd-position digits. If the answer is either zero or eleven (ignoring sign) then the original number is exactly divisible by eleven.
25
To multiply a number by 25: append two trailing zeros, halve the result and halve it again.
To divide a number by 25: double the number, double it again, then shift the decimal point two places to the left.
50
To multiply a number by 50: append two trailing zeros and halve the result.
To divide a number by 50: double the number then shift the decimal point two places to the left.