4th Class Mathematics Decimals and Fractions Decimals

   Decimals

A decimal number is broadly divided into two parts.

(i) Whole number part

(ii) Decimal part The two parts are separated by a dot (.) called the decimal point. From the decimal point as you move on the left the place value is multiplied by 10 and as you move on the right it is divided by 10.  

Look at the following circle:

It is divided into ten equal parts. Out of which two parts are shaded. We say, two tenth of the whole is shaded. Two tenth is written as\[\frac{2}{10}\]. We also write\[\frac{2}{10}\]as 0.2 and read as zero point two.

Here three parts out often equal parts are shaded. So\[\frac{3}{10}\]part is shaded. We read\[\frac{3}{10}\]as three tenths. It can also be written as 0.3 and read as zero point three.

Note: 0.2 can also be written as simply .2 and read as point two. But while writing a decimal we place a zero left to the point if the decimal has no whole number part. It does not make any difference and value of the decimal remains same.

\[\frac{4}{10}=.4=0.4\]                 

\[\frac{5}{10}=.5=0.5\]

\[\frac{6}{10}=.6=0.6\]                 

\[\frac{8}{10}=.8=0.8\]

\[\frac{9}{10}=.9=0.9\]  

 Tenths

• One part of a whole, which is divided into 10 equal parts, is one-tenths of the whole. 
• One - tenths\[\frac{1}{10}=0.1\]It is read as zero point one. Similarly,
• Three tenths\[\frac{3}{10}=0.3\]It is read as zero point three
• Four tenths\[\frac{4}{10}=0.4\]It is read as zero point four  

                                                                                                Look the following table  

Diagram	Shaded Part	Fraction	Decimal
	Five-Tenth	\[\frac{5}{10}\]	0.5
	Eight-Tenth	\[\frac{8}{10}\]	0.8
	Six-Tenth	\[\frac{6}{10}\]	0.6

 Hundredths

One part of a whole, which is divided into 100 equal parts, is one-hundredths part of the whole.

One - hundredths\[\frac{1}{100}=0.01\]

It is read as zero point zero one. Similarly,

Two - hundredths\[=\frac{2}{100}=0.02\]

It is read as zero point zero two.

Three-hundredths\[=\frac{3}{100}=0.03\] Ø  It is read as zero point zero three.  

Look at the following table:

  Thousandths

• One part of a whole which is divided into 1000 equal parts is one-thousandth of the whole.
• One - Thousandths\[=\frac{1}{1000}=0.001\]It is read as zero point zero zero one Similarly
• Two - Thousandth\[=\frac{2}{1000}=0.002\]. It is read as zero point zero zero two.
• Nine - Thousandths\[=\frac{9}{1000}=.009\]. It is read as zero point zero zero nine.
• Twenty five - Thousandths\[=\frac{25}{1000}=.025\]. It is read as zero point zero two five.  

  Ten Thousandths

One part of a whole which is divided into 10000 equal parts is one-ten thousandths of the whole.

• One - Ten thousandths\[=\frac{1}{10000}=0.0001\]. It is read as zero point zero, zero, zero, one.
• Two - Ten thousandths\[=\frac{2}{10000}=0.0002\]. It is read as zero point zero, zero, zero, two.
• Three thousandths\[=\frac{3}{10000}=.0003=0.0003\]it is read as zer0 point zero, zero, zero, three.  

Look at the following table:  

The number given in the place value chart can be written\[\text{4}000+\text{4}00+40+\text{4}\]. We notice, as we move right in the place value chart the value of the place gets one-tenths of the previous one.

So far we have studied the place value chart which has unit place in extreme right side. Now we will know about the decimal place value chart which goes right to the unit place  

  Decimal Place Value Chart                

How many decimal places does the decimal, indicated in the place value chart, has?

Solution:

The decimal indicated in the above table is 0.86. It has two digits right to the point so it has two decimal place.  

  Expanded form of Decimals  

• 42 = 4 tenths and 2 hundredths\[=.\text{4}+\]\[.0\text{2}=\frac{4}{10}+\frac{2}{100}\]
• .705 = 7 tenths, O hundredths and 5 thousandths \[=.7+0+.005=\frac{7}{10}+\frac{0}{100}+\frac{5}{1000}\]
• 34.196 = 3 tens, 4 ones, I tenths, 9 hundredths and 6 thousandths. \[\text{3}0+\text{4}+.\text{1}\]\[+.0\text{9}+.00\text{6}=3\times 10\times +4\times 1+\frac{1}{10}+\frac{9}{100}+\frac{6}{1000}\]
• Write\[\text{4}+.\text{2}+.0\text{4}\]in short form.\[\text{4}+.\text{2}+.0\text{4}\]\[=\text{4}.\text{24}\]
• Write\[3+\frac{2}{10}+\frac{6}{100}\]in short form.\[3+\frac{2}{10}+\frac{6}{100}=3.26\]  

  Like Decimals

The decimals having equal number of decimal places are called like decimals.  

\[0.\text{125},\text{ 75}.\text{235},\text{ 798}.0\text{23},\text{1}.\text{112}\]are like decimals because they have same decimal places.  

  Unlike Decimals

The decimals which have different decimal places are called unlike decimals.  

\[\text{12}.\text{125},\text{ 5}.\text{25},\text{ 79}.\text{8},\text{ }0.\text{6462525},\]are unlike decimals because they have different decimal places.  

   Equivalent Decimals

The decimals which have the same value are called equivalent decimals.  

4.5 and 4.500 are equivalent decimals.  

Are 536.3 and 53.63 equivalent decimals

Solution:

536.3 and 53.63 are not equivalent decimals. Because they have different values.