Decimals and Place Values

Hello children, let us discuss about decimals in mathematics from CBSE sample papers.

Decimals numbers are commonly used in all walks of our life such as business, medicine, measurement, mass, unit, and currency. (also read on properties of decimal numbers)
Decimals are part of a type of numbers in mathematics called as mixed numbers. A mixed number is combination of whole number and decimal part values.
Place value: The value of a digit is determined by its position in a number which is called place value. Place value is used to indicate the position of number system.
The place values are called as following
1-one
  10 – Ten
  100 – hundred
 1000- Thousands
10000- Ten thousands
100000- hundred Thousands
1000000-million
10000000-ten million
100000000-hundred million
1000000000-billion



Place value of decimal point:
                                                     The following table is representing the place value of decimal point values.

10 = 101 Tens

1 Ones

. Decimal point

1/10 = 10-1 Tenths

1/100 = 10-2 Hundredths

1/1,000=10-3 Thousandths

1/10,000=10-4 Ten thousandths

 Here 10¹ represent the tens place value of whole number system.
10⁰ represent the ones place value of whole number system.
’.’ represents the decimal point number.
10^-1 represents the tenths place value of decimal number system
10^-2 represents hundredths place value of decimal number system
10^-3 represents thousandths place value of decimal number system
10^-4 represents ten thousandths place value of decimal number system.



Let’s see the example: find out decimal point value of this given number 12.768

Sol:  here we have given number 12.768

We start from 1 number
Here 1 represents the type of whole number its place value is tens then original number is 1*10=10
Now start with number 2
Here 2 represent the type of whole number its place value is ones then original number is 2*1=2
Decimal point is separates the whole number.
Third number 7 is represent the type of decimal number and its place value is tenths then original value of 7 is   7*0.1=0.7
Fourth number i6 is represent the type of decimal number and its place value hundredth then the original value of 6 is 6*0.01=0.06
Fifth number 8 is represent the type of decimal number and its place value thousandths then the original value of 8 is 8*0.001=0.008


Let’s see the above example in expanded form:
Sol: given number is 12.768
12.768=    12+ 7/10+6/100+8/1000
So, 12.768 has one tens, two unit, seven tenths, six hundredth, eight thousandths


Let’s see the other example:
Ex: find the place value of this numbers: 456, 0.456,54
Sol:  let‘s see first number: 456
4 numbers is hundred place
         5 number is tens place
      6 ones place

Now we see Second number: 0.456
4 number tenths place
5 number hundred’s place
6 number thousand’s place

See the third number: 54
5 number tens place
4 ones place

In upcoming posts we will discuss about Order of Operations in Grade V. Visit our website for information on algebra help