Math & Basic Calculators

Basic addition and subtraction is fine with the plain calculator, but once trigonometry or logarithms enter the picture you need the scientific calculator. When comparing two values, keep percentage (rate of change) and ratio (proportional split) apart — one answers "how much did it rise", the other "how do I split 3:2".

The fraction calculator shows the full reduction and common-denominator steps, not just the result, and the GCD/LCM calculator returns both values the moment you enter two numbers. Binary, octal and hex conversions — common in programming and networking — are handled by a single radix converter, and the logarithm calculator accepts any base, useful for log base 2 or natural log.

The rounding calculator rounds, ceils or floors at any digit you choose (tens place, second decimal, etc.), which comes in handy for quotes and settlement documents, while the average calculator sums and averages a whole list of numbers at once — handy for grades or quick statistics.

Percentages depend on the base. A rise from 100 to 120 is 20 percent, while the fall from 120 back to 100 is about 16.7 — the same absolute change with a different ratio because the denominator moved, which is where consecutive discounts and mark-ups commonly go wrong.

Percent and percentage point differ. A rate moving from 3 to 4 percent is a one point rise and roughly a 33 percent increase; when reporting mixes the two the impression changes sharply, so it is worth checking which is meant.

An average represents but does not describe a distribution. A single extreme value can pull it far, so for skewed data such as income or prices the median sits closer to lived experience — and a wide gap between the two signals that skew.

Rounding regularly causes trouble in settlement documents. The digit chosen and whether values are rounded up or down shift the total, and rounding each line before summing differs from rounding the sum once. Stating the rule in the contract avoids the argument.

Fraction work needs the common-denominator and reduction steps visible to catch errors. Converting to decimals accumulates error on repeating values, so where exactness matters the fraction is safer kept intact.

Greatest common divisor and least common multiple locate where cycles align. Given two schedules recurring every so many days, their least common multiple is the interval at which they coincide, while the largest group size dividing a quantity evenly is the greatest common divisor.

Radix conversion belongs to programming and networking: binary for bitwise operations and permission bits, hexadecimal for colour codes and memory addresses. The same value merely written in another base, the magnitude is unchanged.

Logarithms turn multiplication into addition. Because they express growth as digits, they suit quantities spanning wide ranges such as sound intensity or earthquake magnitude, and they appear when solving for the time compounding takes to multiply a principal.

Ratio problems split by how the division works. Apportioning a whole in a given ratio differs from comparing two values, and in apportionment the sum of the ratio terms becomes the denominator: dividing three to two means splitting into five parts, not handing out three and two.

Powers and roots handle the scale of growth and decline. A compound annual growth rate takes the root matching the number of periods, whereas dividing total growth by the period overstates it — quantities that compound call for a geometric mean, not an arithmetic one.