Arithmetic : Decimals

Decimals and Decimal Places

A decimal is the sum of a whole number and a decimal fraction.
The decimal point separates the whole number and the decimal fraction.
For example, 694.823 is a decimal, which is the sum of the whole number 694 and the decimal fraction 0.823
Note that a decimal fraction is special kind of decimal whose whole number is zero.
Also, a whole number is a special kind of decimal whose decimal fraction is zero, e.g., 7 = 7.0

In the decimal system, the position of the decimal point determines the place value of the digits. Thus, each digit in a decimal has a place value.

To the right of the decimal point,

• the first digit represents the tenths decimal place (being the digit that is multiplied by 1/10);
• the second digit represents the hundredths decimal place (being the digit that is multiplied by 1/100);
• the third digit represents the thousandths decimal place (being the digit that is mulitplied by 1/1000); and so on.

For example, 0.83 = 8 × (1/10) + 3 × (1/100) = 8 × (10/100) + 3 × (1/100) = 80/100 + 3/100 = 83/100 ,
0.083 = 0 × (1/10) + 8 × (1/100) + 3 × (1/1000) = 80/1000 + 3/1000 = 83/1000 and
0.803 = 8 × (1/10) + 0 × (1/100) + 3 × (1/1000) = 800/1000 + 3/1000 = 803/1000

To the left of the decimal point,

• the first digit represents the ones or units place (being the digit that is multiplied by 1);
• the second digit represents the tens place (being the digit that is multiplied by 10);
• the third digit represents the hundreds place (being the digit that is multiplied by 100);
• the fourth digit represents the thousands place (being the digit that is mulitplied by 1000); and so on.