Decimal and Fraction

History of decimal fractions

According to Joseph Needham, decimal fractions were first developed and used by the Chinese in the 1st century BC, and then spread to the Middle East and from there to Europe.The written Chinese decimal fractions were non-positional. However, counting rod fractions were positional.

Qin Jiushao in his book Mathematical Treatise in Nine Sections (1247) denoted 0.96644 by

, meaning

096644

Immanuel Bonfils invented decimal fractions around 1350, anticipating Simon Stevin, but did not develop any notation to represent them.

The Persian mathematician Jamshīd al-Kāshī claimed to have discovered decimal fractions himself in the 15th century, though J. Lennart Berggren notes that positional decimal fractions were used five centuries before him by Arab mathematician Abu’l-Hasan al-Uqlidisi as early as the 10th century.

Khwarizmi introduced fractions to Islamic countries in the early 9th century. His representation of fractions was taken from traditional Chinese mathematical fractions. This form of fraction with the numerator on top and the denominator on the bottom, without a horizontal bar, was also used in the 10th century by Abu’l-Hasan al-Uqlidisi and again in the 15th century work “Arithmetic Key” by Jamshīd al-Kāshī.

A forerunner of modern European decimal notation was introduced by Simon Stevin in the 16th century.[1]

To write a decimal fraction, we use a decimal point. A decimal point is a fraction whose denominator s 10 or a power of 10. In decimal, the dot separated the whole numbers part from the fractional part is called the decimal point. In decimal numbers, the number of digits after the decimal point shows the number of decimal places. The number of decimal places corresponds to the number of zeros in the denominator.[2]

Now, let us study how to read decimals number. It is not a difficult thing to read it, you just need to read the numbers before the point, the point, and then read each number followed one by one.

For example:

13.7 (thirteen point seven)

6. 81 (six point eight one)

Converting between decimals and fractions

To change a common fraction to a decimal, divide the denominator into the numerator. Round the answer to the desired accuracy. For example, to change 1/4 to a decimal, divide 4 into 1.00, to obtain 0.25. To change 1/3 to a decimal, divide 3 into 1.0000…, and stop when the desired accuracy is obtained. Note that 1/4 can be written exactly with two decimal digits, while 1/3 cannot be written exactly with any finite number of decimal digits.

To change a decimal to a fraction, write in the denominator a 1 followed by as many zeroes as there are digits to the right of the decimal point, and write in the numerator all the digits in the original decimal, omitting the decimal point. Thus 12.3456 = 123456/10000.[3]

Exercise: Read Out The Following Numbers And Operation!

2.25

765.371

0. 678

9 ÷ 4.5 = 2

6.5 × 42.6 = 276.9


[2] Roza, Yenita dan Arisman Adnan. 2006. English for Basic Mathematics. Cendikia Insani Pekanbaru.

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