Conversions: Decimal, Fraction, Percent
Conversions between decimals, fractions, and percentages are fundamental concepts in mathematics that allow for the representation of numerical values in different forms. A fraction signifies a part of a whole, while a decimal offers a way to express fractions using powers of ten. A percentage, derived from Latin meaning "by the hundred," represents a fraction with a denominator of 100. Historical milestones in the development of these concepts are notable; for instance, the use of decimal fractions dates back to ancient China, and the modern decimal point became common in England by the early 17th century.
To convert between these forms, several straightforward methods can be used. Percentages can be converted to fractions by dividing the percentage by 100 and simplifying. Similarly, converting percentages to decimals involves moving the decimal point two places to the left. Conversely, to convert decimals to percentages, the decimal point is moved two places to the right. Understanding these conversions is crucial for tasks ranging from basic calculations to more complex mathematical applications, making them valuable skills for learners in various contexts.
Conversions: Decimal, Fraction, Percent
The most commonly used conversions in mathematics concern decimals, fractions and percent.
Overview
The use of decimal fractions has been recorded since ancient China. By the year of 1500, decimals were recognized by mathematicians worldwide but weren’t commonly used until Simon Stein of Bruges wrote a book titled De Thiende (1585), which means, the tenth. Stein wrote decimal expressions for fractions by writing the power of ten as a divisor. By 1619, the modern decimal point had become commonly used in England.
A fraction is a numerical quantity that is not a whole number. A decimal is a fraction whose denominator is a power of ten and whose numerator is shown by figures placed to the right of the decimal point. A repeating decimal is a decimal fraction in which a figure or group of figures is repeated indefinitely. A terminating decimal is a decimal that ends or a decimal with a finite number of digits.
A percent is one part in every hundred. During Ancient times in the city of Rome, leader Augustus made a tax of 1/100 on goods known as the centesima rerum venalium. The word "per cent" has Latin roots. It derives from the word per centum, which mean "by the hundred." The cento of the word became the modern percentage sign, which is two circles separated by a horizontal line.
The correlation of fraction, decimal, and percent is illustrated below. The decimal number 7.5 can also be expressed as the fraction 75/100 or as 15%.
Finding Percent
To find 16% of 1,400, first convert the percentage to its decimal form (0.16). The verbal expression "sixteen percent of fourteen hundred" indicates that 0.16 should be multiplied by 1,400, that is, 0.16 × 1,400 = 224. The result (224) is 16% of 1,400.
To answer the question, What is 35% of 80? first, break apart the question. The rate (35%) and the original number (80) are known; the unknown is the comparative number which constitutes 35% of 80. Since the exercise statement is "(a number) is (thirty-five percent) of (eighty)," the variable stands for a number.
Conversely, to discover what percent of 30 is 40, again, break the question apart. The unknown in this problem is the rate or percentage. Since the statement is "(forty) is (the percentage) of (thirty)," then the variable stands for the percentage.
Converting Percent
Converting percent to fractions is a very simple task. First, divide the percent by 100. If the result is not a whole number, multiply both the numerator and and denominator by 10 for each number after the decimal point. Finally, simplify, or reduce, the fraction. For example, to make 80% a fraction, simply make 80 the numerator and 100 the denominator. Then simplify the fraction to 4/5.
To convert percent into decimals, replace the percent sign with a decimal and move it two places to the left. For example, see Figure 1.
Converting Decimals
To convert decimals to percent move the decimal point two places to the right. For example, the decimal .25 converts to the percentage 25%. The decimal 2.69 converts to 269%.
There are three simple steps to convert a decimal into a fraction. First, divide the decimal by 1. Second, multiply both numerator and denominator by 10 for every number after the decimal point. Finally, reduce, or simplify, the fraction. All terminating decimals can be converted to a fraction by counting the number of decimal places, and putting the decimal's digits over 1 followed by the appropriate number of zeros. An example is shown in Figure 2.
To convert a repeating decimal into a fraction, create a variable and make it equal to the repeating decimal (for example, x = .333...). Multiply on each side of the equation by 10 (10x = 3.333...). Subtract x from each side of the equation (9x = 3). Then simplify (x = 3/9, or 1/3).
Converting multi-digit repeating decimals to fractions can be slightly more difficult, but can still be accomplished in a few steps. First, let x equal the repeating decimal to be converted (for example, x = 0.121212...). Second, count the repeating numbers (in this case, two) and move the decimal the same number of places to the right(x = 12.1212...). Third, multiply x by 1 and the number of places you moved the decimal (100x = 12.121212...). Fourth, subtract x from both sides of the equation. Finally, simplify the fraction (x = 4/33).
Converting Fractions
To convert fractions to decimals, find a number you can multiply by the denominator of the fraction to make it 10, 100, or 1000. Then multiply both numerator and denominator by that number. Finally, take only the numerator and insert the decimal point before the number.
Bibliography
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