197 results for “ber”
Find p percent of a number N.
Add all values and divide by how many there are.
A number is even if it divides by 2 with no remainder.
Convert a mixed number to an improper fraction.
The multiplicative inverse of a number.
A number multiplied by itself.
A number multiplied by itself three times.
A number is divisible by 3 if its digit sum is.
A number is divisible by 9 if its digit sum is.
Any nonzero number to the power zero equals one.
Distance of a number from zero, always non-negative.
The nth root of the product of n numbers.
Any nonzero number to the power zero is one.
Count of diagonals in an n-sided polygon.
Powers of complex numbers in trig form.
Number of standard deviations a value is from the mean.
Number of ways to choose r items from n (order irrelevant).
Number of ordered arrangements of r items from n.
Number of unordered selections of r items from n.
Counts many recursive structures such as balanced parentheses.
Maps any real number to the range (0, 1); used in logistic regression.
Faster-moving fluid has lower pressure (energy conservation in flow).
Position and momentum cannot both be known with unlimited precision.
Energy conservation along a streamline.
Predicts laminar vs turbulent flow.
Limit on knowing position and momentum together.
Number of nuclei remaining over time.
Number of moles from mass and molar mass.
Absorbance of light by a solution.
Number of particles from moles.
Number of particles in one mole.
Particles from moles and Avogadro number.
Genotype frequencies in a non-evolving population.
Cells per mL from a counting-chamber average.
Number of divisions over a growth period.
Metabolic rate scales with body mass to the ¾ power.
Reactions catalyzed per enzyme per second.
Rescale each ingredient for a different number of servings.
Total recipe cost divided across the number of servings.
Conservation of energy in fluid flow.
Ratio of true airspeed to the local speed of sound.
Ratio of inertial to viscous forces; characterises airflow over an airfoil.
Ratio of speed to the local speed of sound.
The number of units that must be sold to exactly cover all costs.
Adjust ingredient quantities for a different number of servings.
Number of tiles to cover a floor.
Continuous day count used by astronomers to compare dates.
Number of days separating two calendar dates.
ISO-8601 week of the year (weeks start on Monday).
Day-of-year number (1–366) for a given date.
Number of people per unit area.
Amount remaining after a number of half-lives.
Recursively finds the greatest common divisor.
a and b have the same remainder when divided by m.
Holds when p is prime and gcd(a,p)=1.
Counts integers up to n coprime to n.
Approximates the number of primes below x.
Least common multiple via the greatest common divisor.
Closed form for the sum of the first n natural numbers.
Closed form for the sum of the first n squares.
A number is divisible by 3 if the sum of its digits is.
A number is divisible by 9 if the sum of its digits is.
Every integer is either even or odd.
The sum of the first n cubes equals the square of the sum.
Count of divisors from prime factorization exponents.
Sum of all divisors from prime factorization.
Euclid-Euler form of even perfect numbers.
Numbers one less than a power of two.
Numbers of a special exponential form.
Sum of the first n natural numbers.
The nth perfect square.
The nth pentagonal figurate number.
Each term is the sum of the two before it.
Closed form for the nth Fibonacci number.
Ratio where the whole is to the larger as the larger is to the smaller.
The rule of the famous unsolved Collatz conjecture.
A primality criterion for p.
Number of positions at which two strings differ.
Minimum number of bits to represent n distinct values.
Converts a binary number to decimal.
Convert a decimal number to binary by dividing by 2 and reading remainders.
Convert a hexadecimal number to decimal.
Number of addressable locations for n bits.
Convert a hex number to decimal by positional weights.
Number of operations completed per unit time.
Converts a Beaufort force number into an approximate wind speed.
Relates the number of items in a system to arrival rate and waiting time.
Total revenue is the selling price multiplied by the number of units sold.
Monthly recurring revenue is the number of active subscribers times average revenue per user per month.
Average revenue per user divides total revenue over a period by the number of users.
Overtones of a note are whole-number multiples of the fundamental.
Time for sound to decay 60 dB in a room.
Number of possible keys for a b-bit key.
Aperture f-number is focal length divided by aperture diameter.
Relates flash power, aperture and subject distance.
Ratio of inertia to gravity waves; governs hull resistance.
Number of claims per unit of exposure.
Number of plants from row and plant spacing.
Number of animals per unit of grazing land.
Scales every ingredient up or down for a different number of servings.
Average number of days stock sits before being sold.
Number of usable IPv4 addresses in a subnet with an n-bit prefix.
Fraction of transmitted bits received in error.
Average number of new users each existing user brings in through referrals.
Average number of secondary infections produced by one infected individual in a fully susceptible population.
Actual average infections per case when part of the population is already immune.
Number of patients who must receive a treatment for one additional patient to benefit.
Number of queries needed by Grover's algorithm to find an item in an unsorted database of N entries.
Number of basis states an n-qubit register can be in superposition of simultaneously.
When two elements form more than one compound, the masses of one element combining with a fixed mass of the other are in ratios of small whole numbers.
At the same temperature and pressure, equal volumes of gases contain equal numbers of molecules — so volume is proportional to moles.
X-rays reflected from parallel crystal planes interfere constructively when the path difference is a whole number of wavelengths.
A Vedic sutra for multiplying numbers close to a base (10, 100, 1000, etc.). Works by finding how far each number is from the base.
A general Vedic multiplication method that works for any two numbers. Uses vertical and crosswise multiplication patterns.
Quick method to square any number near 50 using the identity (50±d)² = 2500 ± 100d + d².
Instantly square any number ending in 5. Multiply the tens digit by (tens digit + 1), then append 25.
Transform numbers with large digits (6-9) into "vinculum" form using complements from 10, making calculations easier.
Instantly multiply any two-digit number by 11 by splitting and adding the digits.
Quickly check if a number is divisible by 2 through 12 without dividing.
Use the identity (a+b)(a-b) + b² = a² to square numbers quickly by going to the nearest easy number.
Multiplying any number by a string of nines is instant: subtract 1 from the number for the left part, then take the complement for the right part.
When numbers are near a convenient working base that is a multiple of a power of 10, use a proportional base to simplify the multiplication.
The Dwandwa (duplex) method squares any number by summing duplex values digit by digit — a general Vedic squaring technique.
Multiply by 10 and subtract the original number — much faster than multiplying by 9 directly.
For numbers a little above 100, use the surplus from 100 to multiply almost instantly.
Use (a+1)² = a² + 2a + 1. Square the round number below, add twice it, add 1.
Gauss's formula: the sum of the first n whole numbers is n(n+1)/2 — no adding required.
The sum of the first n odd numbers is always a perfect square, exactly n².
Two numbers equally spaced around a middle value m multiply to m² − d², using the difference of squares.
Multiply miles by 1.6 for km, or divide km by 1.6 for miles. Consecutive Fibonacci numbers are handy approximations.
Bracket the number between two perfect squares, then refine with a quick average step.
Round the total up to a friendly number, divide by the number of people, then adjust down slightly.
Instantly multiply two numbers that share the same tens digit and whose units digits add up to 10 (e.g. 43 × 47, 62 × 68).
Square any number close to 100 (or 1000) in seconds using how far it sits from the base.
Square any number ending in 9 by leaning on the next round ten, which is much easier to square.
Any two-digit number times 101 is simply the number written twice — no working needed.
Multiply by 12 by using the easy ×10 and then adding twice the number — the same idea extends to 13 and 14.
Add up 2 + 4 + 6 + … up to the Nth even number instantly with a single multiplication.
Extend the ×11 trick to three-digit numbers by adding each neighbouring pair of digits.
Multiply any two numbers from 11 to 19 in your head with a quick three-step pattern.
Multiply two numbers close to 1000 using their deficits from the base, just like the near-100 trick.
Reverse the digits of any two-digit number and subtract — the result is always 9 times the difference of the digits.
For any whole number, the product of the number before it, itself and the one after, plus the number, equals its cube.
Multiplying by 1.5 is simply adding half of the number to itself — handy for recipes and time-and-a-half pay.
Multiply any number by a repunit of 9s (99, 999, 9999…). Split the answer into two halves: left half = number − 1, right half = complement of left half to all 9s.
The general Vedic sutra for multiplying any two numbers. Work digit by digit: units × units, then cross-multiply, then tens × tens — carrying as needed.
A Vedic method for dividing by numbers close to a power of 10. Use the complement as a "flag" and perform synthetic-style division mentally.
Factor quadratics instantly: for x² − (a+b)x + ab = 0, find two numbers whose sum equals the middle coefficient and whose product equals the constant term.
Divide large numbers by multi-digit divisors using a flag (the non-leading digits of the divisor). Process one digit at a time, subtracting flag × quotient digit as you go.
When adding a number close to a round number, add the round number first, then subtract the small difference. Much easier mentally.
When two numbers are equidistant from a round "anchor" number, use the difference-of-squares identity: (anchor + d)(anchor − d) = anchor² − d².
Multiply by rounding one factor to the nearest easy number, then adjusting. For example, 48 × 7 = 50 × 7 − 2 × 7.
Subtract from a round number by using the complement trick: subtract from (round number − 1) instead, then add 1. All digit subtractions become from 9.
Square any number by rounding to the nearest multiple of 10: n² = (n+d)(n−d) + d², where d is the distance to that multiple.
The average of any evenly spaced (arithmetic) sequence is simply (first + last) ÷ 2. No need to add all terms.
Multiply any number by 99 using: n × 99 = n × 100 − n. Just append two zeros and subtract the original number.
Multiply a two-digit number by 111: n × 111 = n × 100 + n × 11. Use the multiply-by-11 trick for the second part.
Since 37 × 3 = 111, multiply by 37 by first dividing the other number by 3, then multiplying by 111. Works perfectly when the number is divisible by 3.
Divide by 8 by halving the number three times in a row. Since 8 = 2³, three successive halvings give the exact answer.
To square any number ending in 5: multiply the tens digit by (tens digit + 1), then append 25. Works instantly for any size.
When both numbers are close to 100, use their deficits: cross-subtract to get the hundreds, multiply deficits for the units.
Cube a number near 10 using the binomial expansion: (10 + a)³ = 1000 + 300a + 30a² + a³. Compute each piece and add.
Sum = n × (first + last) / 2, where n is the number of terms. Find n using: n = (last − first) / common difference + 1.
Sum = a(rⁿ − 1) / (r − 1) where a is the first term, r is the common ratio, and n is the number of terms.
Multiply any number by 6 by first multiplying by 3 (easy), then doubling the result. Two simple steps instead of one hard one.
Multiply by 3 by doubling the number and adding the original once more.
Split 13 into 10 + 3: multiply by 10, then add three times the number.
Split 14 into 10 + 4: multiply by 10, then add four times the number.
Since 16 = 2⁴, multiply by 16 by doubling the number four times in a row.
Use 95 = 100 − 5: multiply by 100, then subtract five times the number.
Use 105 = 100 + 5: multiply by 100, then add five times the number.
Use 110 = 100 + 10: multiply by 100, then add ten times the number.
Any 3-digit number × 1001 just repeats itself: abc × 1001 = abcabc.
Multiplying by 0.5 is the same as halving the number.
For n near 200: n² = 200² + 400×d + d², where d = n − 200 (d can be negative).
Split as (a + b)² = a² + 2ab + b², taking a as the round hundreds part and b the rest.
Divide by 4 by halving the number twice.
Instead of taking away, count up from the smaller number to the larger one — easier for making change.
The average of two numbers is their midpoint: add them and halve. Or take the lower and add half the gap.
Round each number to a friendly value, compute, then note the direction of error for a quick sanity check.
Add a big number in friendly chunks instead of all at once, keeping a running total.
Add or subtract a nearby round number, then correct by the small difference.
The complement of a 2-digit number to 100: subtract the tens digit from 9 and the units from 10.
Round the divisor and dividend to compatible numbers that divide evenly for a fast estimate.
To find a fraction of a number, divide by the denominator, then multiply by the numerator.
Round both numbers to multiples of ten, multiply, then subtract the cross-correction for a close estimate.
When numbers are close, multiply one by the count and adjust by the small differences from it.
When two numbers are close, just find the gap directly instead of full subtraction.
For ax² + bx + c = 0, x = (−b ± √(b² − 4ac)) ÷ 2a. The discriminant b²−4ac tells you the number of real roots.
For two positive numbers, (a + b)/2 ≥ √(ab). Equality only when a = b.
1³ + 2³ + ... + n³ = (n(n+1)/2)² — the square of the nth triangular number.
Add the place values (1, 2, 4, 8, ...) wherever there is a 1.
Repeatedly divide by 2 and record remainders bottom-up.
Add values left to right; when a smaller numeral precedes a larger one, subtract it.