Percentage

In mathematics, a percentage (from Latin per centum 'by a hundred') is a number or ratio expressed as a fraction of 100.

[3] For example, 45% (read as "forty-five percent") is equal to the fraction ⁠45/100⁠, the ratio 45:55 (or 45:100 when comparing to the total rather than the other portion), or 0.45.

In Ancient Rome, long before the existence of the decimal system, computations were often made in fractions in the multiples of ⁠1/100⁠.

For example, Augustus levied a tax of ⁠1/100⁠ on goods sold at auction known as centesima rerum venalium.

Many of these texts applied these methods to profit and loss, interest rates, and the Rule of Three.

[6][7] The sign for "percent" evolved by gradual contraction of the Italian term per cento, meaning "for a hundred".

The "cento" was contracted to two circles separated by a horizontal line, from which the modern "%" symbol is derived.

For example, 50% of 40% is: It is not correct to divide by 100 and use the percent sign at the same time; it would literally imply division by 10,000.

Because of the commutative property of multiplication, reversing expressions does not change the result; for example, 50% of 20 is 10, and 20% of 50 is 10.

The calculation of percentages is carried out and taught in different ways depending on the prerequisites and requirements.

The reason for this apparent discrepancy is that the two percent changes (+10% and −10%) are measured relative to different initial values ($200 and $220, respectively), and thus do not "cancel out".

For example, if a party obtains 41% of the vote and this is said to be a 2.5% increase, does that mean the earlier result was 40% (since 41 = 40 × (1 + ⁠2.5/100⁠)) or 38.5% (since 41 = 38.5 + 2.5)?

is still in use in the highly formal language found in certain documents like commercial loan agreements (particularly those subject to, or inspired by, common law), as well as in the Hansard transcripts of British Parliamentary proceedings.

However the titles of bonds issued by governments and other issuers use the fractional form, e.g. "3+1⁄2% Unsecured Loan Stock 2032 Series 2".

In line with common English practice, style guides—such as The Chicago Manual of Style—generally state that the number and percent sign are written without any space in between.

The practice is probably related to the similar way that batting averages are quoted.

As "percent" it is used to describe the grade or slope, the steepness of a road or railway, formula for which is 100 × ⁠rise/run⁠ which could also be expressed as the tangent of the angle of inclination times 100.

This is the ratio of distances a vehicle would advance vertically and horizontally, respectively, when going up- or downhill, expressed in percent.