Decimal Fraction
A decimal fraction is a way of expressing a fraction in decimal form, where a non-whole number is represented by a point (decimal) followed by digits that indicate parts of a whole. Both decimals and fractions serve to describe portions of a whole number and are mathematically equivalent; for instance, the fraction 1/2 is the same as 0.5. The conversion between the two formats involves understanding place values, such as tenths, hundredths, and thousandths. To convert a fraction to a decimal, one typically divides the numerator by the denominator. For example, the fraction 3/4 converts to the decimal 0.75, which can also be expressed as seventy-five hundredths. These concepts are widely applicable in everyday situations, ranging from cooking and budgeting to scientific research and construction. Understanding how to convert between fractions and decimals is crucial for accurate measurements and calculations in various fields.
Subject Terms
Decimal Fraction
Fractions have been used since ancient times for portioning and dividing a whole into parts. Fractions and decimals mathematically are the same in systematic structure and purpose in the sense that they both are part of a whole number. Therefore, a decimal can be considered equivalent to a fraction and vice versa if they both are of equal value. In order to determine the equivalency of a decimal and a fraction, they must be converted into equal terms or measurements.
Overview
According to a study conducted at the University of California, fractions made their first systematic appearance in ancient Egypt. Fractions were used in the Egyptian bartering system. Instead of using currency, Egyptians rationed and portioned food and other goods during transactions. The U.S. dollar is equal to one hundred cents. Dividing the dollar into quarters (or 4/4) results in four piles of twenty-five cents each, or $.25.
Decimals and fractions are used in everyday life ranging from recipes, scientific investigations, customer sales, manufacturing, and construction. The understanding of converting fractions to decimals can make a significant difference between using appropriate measurements when creating a model, structure, or device.
To convert a fraction to a decimal, one must first be familiar with place value of decimals. For example, the number 3.67 can be read as three and sixty-seven hundredths. It is rewritten as a fraction exactly as it is spoken:
The 67/100 fraction is the ratio of 67 out of 100.
Fractions use the place values of tenths, hundredths, thousandths, and so on. If the decimal number is 0.6, or six tenths, the fraction will be 6/10, or 3/5 in simplest form. The decimal number .07 would be seven hundredths, or 7/100.
Converting a Fraction to Decimal Number
First, divide the numerator into the dominator. The horizontal line between two numbers of a fraction represents a divisor symbol. In this case, 3 divided by 4 is decimal number 0.75. The decimal number 0.75 can be verbally expressed as seventy-five hundredths. Seventy-five hundredths converted as a fraction in numeric form is 75/100, or in simplest form is 3/4.
Before dividing this fraction to find the decimal, it first needs to be in its simplest form 16/20 in simplest form is 4/5. Now the fraction is ready to be divided. The result, 0.8, is verbally expressed as eight tenths, that is, 8/10, or in simplest form 4/5.
Bibliography
Martinie, Sherri L. "Decimal Fractions: An Important Point." Mathematics Teaching in the Middle School 19.7 (2014): 420-429.
McKellar, Danica. "How to Entertain Yourself While Babysitting a Devil Child." Math Doesn’t Suck. New York: Plume, 2008.
Shaughnessy, Meghan Mary. Students' Flexible Use of Multiple Representations for Rational Number: Decimals, Fractions, Parts of Area, and Number Lines. Berkeley: UC Berkeley P, 2009.
Wang, YunQi, and Robert Siegler. "Representations of and Translation Between Common Fractions and Decimal Fractions." Chinese Science Bulletin 58.36 (2013): 4630-4640.