Reading and Writing Decimal Numbers

Decimal numbers can be written in various ways; for example, 0.25 can be written as $\frac{25}{100}$ or $\frac{1}{4}$ . When writing a decimal number in decimal form, a decimal point is used to separate the whole numbers from the decimal part. Whole numbers are decimal numbers where the decimal part is equal to zero; they can be written without a decimal point.

I. Reading decimal numbers

To read decimal numbers correctly, you just need to locate the place value for each digit in standard decimal form.


This table gives the names of the digits according to their place value in relation to the decimal point.

Examples:
The number 504.36 is read as 504 units and 36 hundredths.
The number 47.8951 is read as 47 units and 8,951 ten thousandths.

II. Writing decimal numbers

A. Group the digits into threes

Large numbers are written slightly differently in different books and in different countries. To make them easier to read, the digits can be split up into groups of three. These groups can then be separated using commas.


In the United States, the whole part of a decimal number is written by grouping the digits into threes in a line moving from the left of the decimal point if there is one, and putting commas between each of these groups.


Examples:
“Eighty-six million seven hundred ten thousand thirteen” is written as 86,710,013.
“Eight thousand three units and sixty-nine hundredths” is written as 8,003.69.


The decimal part of a decimal number can also be written by grouping the digits into threes starting just after the decimal point and moving to the right. However, in these math help tutorials, we will just write all of the decimal part of the number together.


Examples:
“Three hundred twelve thousandths” is written as 0.312.
“Seven thousand and twenty-five hundred thousandths” is written as 7,000.00025.

B. Using decimal fractions

It is possible to use decimal fractions to write decimal numbers.


Example: 6.789 can also be written as $6+\frac{7}{10}+\frac{8}{100}+\frac{9}{1000}$ , or $\frac{6789}{1000}$ , or even $6+\frac{789}{1000}$ .

III. A little history

The first known European work to have addressed decimal numbers appeared in 1585 and was called La Thiende (The Tenth); its author, Simon Stevin, was a Flemish mathematician. The notation that he proposed was quite complex, and used a particular symbol to denote units, another for tenths, yet another for hundredths, and so on.


In 1592, the Swiss clockmaker and mathematician Jost Bürgi simplified Stevin’s notation by using the ° sign to signify the units digit.
Example: the number 54.306 was written 54°306.


The Italian Magini perfected the notation introduced by Bürgi by replacing the small circle (°) with a point placed between the units digits and the tenths digit. Thus the Anglo-Saxon decimal notation was born.
Example: the number 54.306, as it is written today


In 1605, the Dutch mathematician Willebrord Snellius came up with the comma notation that is now used in some countries, such as France. For example, the number 54.306 would be written as 54,306.

Read more:
Multiplying or Dividing a Decimal Number by 10, 100, or 1,000
Multiplying Decimal Numbers
Dividing Decimal Numbers
Converting Decimals to Fractions
The Effect of Addition and Multiplication on the Order of Numbers
Describing Different Types of Numbers
Dividing Whole Numbers with a Remainder
Comparing and Ordering Decimal Numbers
Adding and Subtracting Decimal Numbers