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

Whole Numbers and Place Value in Grade V

Hello friends,Previously we have discussed about probability worksheets and  today we are going to discuss one of the important topics of math grade V of cbse syllabus which is whole numbers and place value. Whole numbers are the set of familiar numbers (0, 1, 2, 3, 4, and so on). When they are called counting numbers, zero is not included. The whole numbers are also called the positive integers (or the nonnegative integers, if zero is included) and they plays an important role to solve math problems.
The numbers 0, 1, 2, 3, ... etc.

There is no or decimal part and no negatives. We will begin our review of place values with a look at whole numbers. When writing large numbers it is a common practice to separate them into groups of three using commas as the separator. When separating into groups of three, start from the right and count toward the left.
Example: 3, 79 and 980 are all whole numbers.
Place value is the value of a digit as determined by its position in a number. The name of the place or location of a digit in a number. The ability to understand place values is an important mathematics skill measured in the Early Childhood Longitudinal Study. More specifically, students should be able to identify place values in integers to the hundreds place to achieve this skill. Simply the Place Value is the position of a digit in a number written in standard form determines the actual value the digit represents.This table shows the place value for various position (want to Learn more about Whole Numbers ,click here),

Place (underlined)	Name of Position
1 000	Ones (units) position
1 000	Tens
1 000	Hundreds
1 000	Thousands
1 000 000	Ten thousands
1 000 000	Hundred Thousands
1 000 000	Millions
1 000 000 000	Ten Millions
1 000 000 000	Hundred millions
1 000 000 000	Billions

We will take some examples for explanation.
Example:
The number 521092 has a 5 in the hundred thousands place, a 2 in the ten thousands place, 1 in the thousands place, 0 in the hundredths place, 9 in the tens place, and a 2 in ones place.
Example:
Four billion, sixty million, six hundred twenty thousand
4,060,620,000
And another example
9,568,125
Numbers, such as 9,568,125 have seven digits.  Each digit has a different place value.
The first digit is called the millions' place value. There are nine millions in the number 9,568,125
The second digit tells you how many sets of one hundred thousand are in the number.  The number 9,568,125 has five hundred thousand.
The third digit is the ten thousands' place. There are six ten thousands in addition to the nine millions and five hundred thousand.
The fourth digit is the one thousands' place which is eight in this example.
The fifth digit is the hundreds' place which is one in the number 9,568,125.
The next digit two is the tens' place.
The last or right digit is the ones' place which is five in this example.
Therefore, there are nine sets of 1,000,000, five sets of 100,000, six sets of 10,000, eight sets of 1000, one sets of 100, two sets of 10, and 5 ones in the number 9,568,125.

Example :In the numeral 7,015,384, what digit is in the...
  Ques                                                           Answer
a) Ones place ?                                                   4
b) ten thousands place ?                                     1
c) tens place ?                                                     8
d) millions place ?                                               7
e) hundreds place ?                                            3
f) hundred thousands place ?                             0
g) thousands place ?                                           5
So here we end with whole numbers and place value. I hope that this article will help you in solving problems related to whole numbers and place value and if anyone wants to know about Number systems in Grade V and Percentages in Grade VI then they can refer Internet.