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Expressing fractions, decimal numbers and percentages.
Fractions, decimals, and percentages are different ways of expressing numerical quantities and proportions.
For example, one half, 0.5, and fifty percent represent the same numerical value.
A common fraction expresses a part of a whole using a numerator and denominator.
Examples include one half, one third, two thirds, and three quarters.
The numerator of a fraction is normally read as a cardinal number.
For example, 2/3 begins with two, 5/8 begins with five, and 11/20 begins with eleven.
The denominator is commonly expressed using an ordinal number when the numerator is one and often a pluralized ordinal when the numerator is greater than one.
For example, one third, two thirds, one fifth, and three fifths.
The fraction 1/2 is normally read as one half or a half, while more than one half is expressed with halves.
For example, one half, a half, and three halves.
The fraction 1/4 can be read as one quarter or a quarter, while larger quantities use quarters.
For example, one quarter, a quarter, and three quarters.
Some denominators use irregular or modified ordinal forms.
Important examples include half, third, fifth, eighth, ninth, and twelfth.
A mixed number combines a whole number with a proper fraction.
For example, one and a half, two and three quarters, and five and one third.
And is normally used between the whole-number part and the fractional part when a mixed number is spoken.
For example, two and a half and seven and three quarters.
Fractions can modify nouns to express a quantity or proportion.
For example, a half hour, a three-quarter mile journey, and a two-thirds majority.
A fraction used directly before a noun as a compound modifier is commonly hyphenated.
For example, a two-thirds majority, a three-quarter-mile walk, and a one-half-hour delay.
The noun following a fraction depends on whether the fractional quantity refers to a singular or plural amount.
For example, half of the cake is left, but two thirds of the students are absent.
Verb agreement after a percentage expression depends on the noun phrase following of.
For example, Thirty percent of the water is gone, but Thirty percent of the students are absent.
Decimal numbers are normally read using the word point between the whole-number and fractional parts.
For example, 3.14 is three point one four.
Digits after a decimal point are normally read individually rather than as an ordinary whole number.
For example, 4.05 is four point zero five.
Zero after a decimal point is normally pronounced when it is necessary to make the digit sequence clear.
For example, 0.5 is zero point five and 2.05 is two point zero five.
A decimal less than one can be read with zero before the decimal point.
For example, 0.75 is zero point seven five.
English normally uses a point as the decimal separator, although other languages may use a comma.
For example, English writes 3.5 rather than 3,5.
Decimal quantities can take singular or plural nouns depending on the noun and the specific quantity being described.
For example, 1.5 hours is plural, while 1.0 hour can be used when exactly one unit is intended.
A percentage is normally read as the number followed by percent.
For example, 25% is twenty-five percent and 3.5% is three point five percent.
Percent normally follows a numerical value, while percentage is a noun referring to the proportion itself.
For example, twenty percent of users and What percentage of users?
Percent is normally used directly after a numerical value.
For example, ten percent, 10%, and half a percent.
A percentage of introduces the group or quantity from which the proportion is calculated.
For example, A percentage of the students were absent.
A percentage point measures the absolute difference between two percentages.
For example, an increase from 20% to 25% is an increase of five percentage points.
A relative percentage increase is different from a difference measured in percentage points.
For example, an increase from 20% to 25% is five percentage points but a twenty-five percent relative increase.
The percent sign is common in numerical, technical, and tabular writing, while the word percent may be preferred in running prose depending on style.
For example, 25% in a table and twenty-five percent in ordinary prose.
A fraction can be expressed as a decimal when its numerical value is represented in decimal form.
For example, one half equals zero point five and one quarter equals zero point two five.
A fraction can be expressed as a percentage by representing its proportion per hundred.
For example, one half is fifty percent and one quarter is twenty-five percent.
A decimal can be expressed as a percentage by interpreting it as a proportion per hundred.
For example, zero point five is fifty percent and zero point two five is twenty-five percent.
Percentages can modify a noun phrase introduced with of to express a proportion of a group or quantity.
For example, Fifty percent of the students were present and Twenty percent of the water was lost.
Expressions such as more than, less than, under, and over can modify percentages to indicate approximate or bounded proportions.
For example, more than 50 percent, under 10 percent, and over 90 percent.
Approximately and about can indicate that a percentage is not exact.
For example, approximately 30 percent and about 15 percent.
A decimal with a recurring sequence can be described using repeating or recurring terminology.
For example, 0.333... is approximately zero point three three three recurring.
Fractions and decimals can form ranges using from ... to, between ... and, or numerical punctuation.
For example, between 0.5 and 1.5 and from one half to three quarters.
Use correct fraction names, decimal pronunciation, percentage terminology, noun agreement, and distinctions between percentage points and relative percentages.
Common mistakes include saying two third instead of two thirds, confusing percent with percentage, reading decimal digits as a whole number, and confusing percentage points with percentage increases.