What is Decimals?

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Decimals

Decimal number system is a positional notation with base 10. It is used to refer to numbers that have a fractional part separated from the integer part with decimal separator. Decimals help us to write fractional numbers without writing a fraction with numerator and denominator.

Decimal place value chart

In writing any number, the position of each digit is very crucial.

 

Thousands
(1000)
Hundreds (100) Tens 
(10)
Ones 
(1)
Decimal point 
(.)

 

Tenths

( \dfrac{1}{10} )

Hundredths 
(\dfrac{1}{100} )
Thousandths (\dfrac{1}{1000}) Ten thousandths 
(\dfrac{1}{10000})

When we move to the right in the above place value chart, the value of digit becomes ten times smaller i.e. one tenth and when we move to the left in the chart, the value of digit becomes ten times bigger.

 

One-tenth

We can write it as 0.1.
One-tenth                                                     

One part of 10 equal parts is one-tenth and written as \dfrac{1}{10} or 0.1.

One – hundredth

We can write it as 0.01
0.01 = \dfrac{1}{100} = \text{One - hundredth}
One-hundredth 

One part of 100 equal parts is one – hundredth and written as \dfrac{1}{100} or 0.01.

One–thousandth

We can write it as 0.001.

Reading and Writing Decimal Fractions

Every decimal number has two parts, a whole/integral part and a decimal part. A dot (.) called decimal point separates the integral and decimal part.

Example.

 43.678 is a decimal fraction and can be represented as 

Placing the above decimal fraction in decimal place value chart.

Thousands
(1000)
Hundreds
(100)
Tens
(10)
Ones
(1)
Decimal point 
(.)
Tenths
(\dfrac{1}{10} )

Hundredths
(\dfrac{1}{100})

Thousandths
(\dfrac{1}{1000})
    4 3 . 6 7 8

The above number read as Forty three point six seven eight or Forty three and six hundred seventy eight thousandth.

Expanded Form of Decimals

By writing decimal in its expanded form, we can show value of each digit.

Writing Decimals in Expanded Form

Step1: Place the number in decimal place value chart.

Step2: Now, write the value of each digit of decimal fraction.

Example 1.
 0.67
Step1: Place the number in decimal place value chart.
Decimal Place Value Chart

Thousands 
(1000)
Hundreds 
(100)
Tens
(10)
Ones 
(1)
Decimal 
Point
(.)
Tenths 
(\dfrac{1}{10})
Hundredths 
(\dfrac{1}{100})
Thousandths
(\dfrac{1}{1000})
Ten thousandths
(\dfrac{1}{10000})
          6 7    

Step2: Now, write the value of each digit of decimal fraction.
6 tenths +7 hundredths.
OR
\dfrac{6}{10}+\dfrac{7}{100}

Example 2.
 0.507
Step1: Place the number in decimal place value chart.
Decimal Place Value Chart

 

Thousands 
(1000)
Hundreds 
(100)
Tens
(10)
Ones 
(1)
Decimal 
Point
(.)
Tenths 
(\dfrac{1}{10})
Hundredths 
(\dfrac{1}{100})
Thousandths
(\dfrac{1}{1000})
Ten thousandths
(\dfrac{1}{10000})
          5 0 7  

Step2: Now, write the value of each digit of decimal fraction.
5 tenths  +7 hundredths
OR
\dfrac{5}{10}+\dfrac{7}{1000}

Example 3.
 478.831
Step1: Place the number in decimal place value chart.
Decimal Place Value Chart

Thousands 
(1000)
Hundreds 
(100)
Tens
(10)
Ones 
(1)
Decimal 
Point
(.)
Tenths 
(\dfrac{1}{10})
Hundredths 
(\dfrac{1}{100})
Thousandths
(\dfrac{1}{1000})
Ten thousandths
(\dfrac{1}{10000})
  4 7 8   8 3 1  

Step2: Now, write the value of each digit of decimal fraction.
4 hundred +70 tens  +8 ones  +3 hundredths  +1 thousandths
OR
 400+70+8+\dfrac{8}{10}+\dfrac{3}{100}+\dfrac{7}{1000}

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