Understanding Decimal Fractions 2

< 17.1 Understanding Decimal Fractions 1 | Topic Index | 17.3 Representing Decimal Fractions >

The following aspects also need to be understood while dealing with decimal numbers.

0 As a Place Holder
 * 1) A 0 at the end of a decimal number like 3.250 can be ignored as it just means  which does not change the value of the number. Hence it can be written as 3.25.
 * 2) This also applies to any continuous string of 000s at the end of a number like in 4.580000
 * 3) In any whole number, there are no parts less than 1. Hence there is no need for a decimal point to show the separation. We can imagine a decimal point at the end of the number. 256 is same as 256.0. The 0 &amp; the decimal point can be left out without any loss of meaning.

What about a number like 267 + 3/10 + 3/1000, where the hundredths place has no numeral? The number can be rewritten as like 267 + 3/10 +0/100   +3/1000. This in turn can be written as 267.303. Hence omitting the 0 between the numerals changes the value of the number.

Nomenclature

The places less than 1 are labelled as follows. The place values of the whole number are given for comparison.

Absence of Oneths

Some may wonder as to why the place value &ldquo;oneths&rdquo; is missing. A little thinking would reveal that &ldquo;Oneths&rdquo; is the same as &ldquo;Ones&rdquo;. Five &ldquo;ones&rdquo; are same as five &ldquo;oneths&rdquo; and their value is 5.

Operations 

Since decimal fractions are like whole numbers, but with a decimal point, all the four operations on decimal fractions are same as those for whole numbers. The important aspect is to keep track of the position of the decimal point. We will see this aspect in detail in a further chapter.

Extension of the Number System

The ability to write all fractions in terms of the decimal place value system enabled a deeper understanding of numbers. They also helped to define various other kinds of numbers like irrational, transcendent, real etc.

Counting Vs Measuring Numbers 

A flock of 23 birds is written as 23 without any decimal point. Here 23 is a counting number.

But while measuring the length of a path, using a meter scale if it is 23 meters, it is written usually as 23.0 meters. In the second case the measurement is nearest to 23 meters and there may be a few millimetres which have been left out. Writing it as 23.0 makes it clear that the length is 23.0 meters measured to the nearest accuracy possible. Here 23.0 is a measuring number.

This difference would be explained to students in Section 24 on Measurement.

< 17.1 Understanding Decimal Fractions 1 | Topic Index | 17.3 Representing Decimal Fractions >