# Decimal Place Values : Concept & Chart

In this post we will understand the concept of decimal place value and the meaning of the terms tenth, hundredths ad thousandth.

After the concept we will move on to solve some questions related to decimal place value which are to the standard of Grade 5

## Place Value Concept Review

Before learning the decimal place value, let us try to review the concept of place value in whole number.

Consider the whole number 479

The place value of the number can be written as:

Here the digits of 479 are represented as:

From the above image you can observe that:
⟹ Digits in Ones places are represented as it is (here 9)
⟹ Digits in Tens places are represented by multiplication with 10 (here 70)
⟹ Digits in Hundred places are represented by multiplication with 100 (here 400)

## Decimal Place Value

Now let us introduce numbers after the decimal point
Let the number be 479.362

From the above image you will observe that:
⟹ Number just after the decimal point is called Tenths place (here 3)
⟹ Second number after the decimal point is called Hundredths place (here 6)
⟹ Third Number after the decimal point is called Thousandth place (here 2)

Let us understand each decimal value in detail

### Tenths Place in Decimal

The number just after the decimal point is the Tenth Place.

The simplest tenth place number is 0.1

In fraction form 0.1 is written as \frac{1}{10}

Understanding Tenth Place using illustration

Let whole number 1 is represented by rectangular box

Now \frac{1}{10} is represented as one tenth part of the rectangular box

Let us look at another example of Tenth decimal place

Example 02
0.6 or ( \frac{6}{10} )

If whole number 1 is complete box, then 0.6 or \frac{6}{10} is six tenth part of the given box

Example 03
Representation of number 2.4

2.4 is made up of two numbers
⟹ whole number 2
⟹ decimal number 0.4 (or \frac{6}{10} )

If whole number 1 is represented by complete box, then 2.4 can be shown as follows:

From the above image you can observe that:
⟹ Whole number 2 is represented by 2 rectangular boxes
⟹ decimal 0.4 is represented by four-tenth part of the box

I hope you now have basic understanding of the tenth place of decimal.
Let us now move to understand the hundredth place of decimal

### Hundredths Place in Decimal

The second place after decimal is the Hundredths Place value.

The simplest Hundredths Place value is 0.01

In the fraction form 0.01 is written as \frac{1}{100}

Hundredths Place Value using Illustration

Let 1 is represented as complete rectangular box.
Then \frac{1}{100} is one hundredth part of the rectangle

Let us see some other examples for conceptual clarity

Example 2
0.37

Let us write 0.35 in fraction form
0.35 ⟹ \frac{35}{100} \frac{35}{100} represents 35th part of the whole box

Example 03
2.42

The number 2.42 is made of two parts
⟹ whole number 2
⟹ decimal number 0.42 ( or \frac{42}{100} )

The number can be illustrated as follows

In the above image you will observe that:
⟹ whole number 2 is represented by 2 yellow boxes
⟹ 0.42 is represented by third box which is 42/100 part of the box

I hope hundredth place value in decimal is also understood by the students.
Let’s now move on to understand the thousandth place value.

### Thousandth Place value in decimal

The third number after the decimal is the thousandth value of the decimal

The simplest thousandth place value is 0.001

The fraction form of 0.001 is \frac{1}{1000}

Understanding Thousandth place using illustration

Let 1 represent the whole cube.
Then \frac{1}{1000} is one thousandth part of rectangle as shown in the image below

In the above image you can see that the cube is divided into thousand parts.
Out of thousand box, only one box is colored in green.
Hence the image represents \frac{1}{1000} part of the cube

Let us look at another example for conceptual clarity

Example 02
0.132

Let us write 0.132 in fraction form
0.132 ⟹ \frac{132}{1000} \\\

If whole number 1 is the complete cube, then \frac{132}{1000} is 132 parts of thousand equal parts.

We are done with conceptual part of decimal place value.
Let us understand the summary of this chapter through decimal place value chart.

### Summary of Tenth, Hundredth & Thousandth Place

The right side of decimal point is the start of decimal place value

Tenth Place (1/10) ⟹ Digit just right of decimal
Hundredth Place (1/100) ⟹ 2nd digit after decimal
Thousandth Place (1/1000)⟹ 3rd Digit after decimal

## Decimal Place Value Chart

The chart will basically tells the place value of any given number.

The chart is basically divided into three segments
(a) Decimal Point
(b) Integer Values (Left side of decimal point)
(c) Decimal Values (Right side of decimal point)

In order to use the chart, the student should have clear understanding of both whole number place value and decimal number place value.

Below is the chart for your reference

Let us understand the use of the chart with the help of example

Example 01
Find the place value of given number with the help of Place Value Chart
12.365

From the above table you can note that:
1 ⟹ is in Tens Place
2 ⟹ Ones Place
. ⟹ decimal point
3 ⟹ Tenth Place
6 ⟹ Hundredth Place
5 ⟹ Thousandth Place

This is how Place Value chart for numbers.
Let us look at another example for conceptual clarity

Example 02
Find the place value of number
⟹ 362.969

From he above table you can note that
3 ⟹ is in Hundreds Place
6 ⟹ is in Tens Place
2 ⟹ Ones Place
. ⟹ decimal point
9 ⟹ Tenth Place
6 ⟹ Hundredth Place
9 ⟹ Thousandth Place

I hope that the concept of decimal place value is clear.
Let us move on to solve some worksheet questions for Math Practice.

## Questions on Place Values in Decimal Numbers

Below is the collection of questions from the topic decimal place values.

All the questions are to the standard of Grade 5 Math.

Each questions are provided with detailed solution.

### Identify the place value of bold digit using Place Value Chart

In the below set of question, a number is given with one bold digit.

You have to identify the place value of that bold digit.
Use the place value chart to find the answer

(a) 679.171

From the above table you can observe that the given digit lies in Hundredth Place

(b) 9274.36

Th given number lies in Hundreds Place

(c) 11.335

The given number lies in Thousandth Place

(d) 852.739

From the table you can see that the number 7 lies in tenth place

(e) 6209.289

The given number lies in Ones Place

(f) 123.005

The given number lies in Hundredths Place

### Place values in Decimal Numbers

Here one number is provided in the question.
You have to identify the right place value digit as asked in the question statement.

(a) In 502.12, which digits is in Tens Place

Number 0 is in Tens Place

(b) For below number, find digit which is in Hundredth Place
1000.250

Number 5 is in Hundredth Place

(c) In 200.21, which digits is in thousandth place

You can see that there is no number given in Thousandth Place.
But you can show number 0 in that empty space, it will have no effect on overall value of the number.

Hence number 0 is in Thousandth Place

(d) For the below number, find the digit in thousand place
9568.1

Hence number 9 is in Thousands Place

(e) For the below number, find the digit in tenths place
1002.365

(f) For the below number find the digit in Hundredth Place
1.203

Digit 0 lies in Hundredth Place

(g) In 3.201, which digit is in thousand place

You can see that there are no digits given in hundreds and thousands place.
You can write digit zero in the empty spaces as it will not change the value of given number.

(h) In 66.397, which digit is in thousandth place

Digit 7 is in the thousandth place

(i) In 140.248, which digit is in ones place

Digit 1 lies in Hundreds Place

(j) For the below number, find digits in hundredth place
0.243

Digit 3 is in Thousandth Place

### Compare Decimals using Grids

In this set of question, an image of rectangular grid is provided.
You have to study the image and find the right decimal that can represent the grid.

(01) Select the decimal for the following grid

(a) 0.4
(b) 0.3
(c) 0.2
(d) 0.5

Total number of boxes = 10
Number of colored boxes = 2

Colored Box Fraction
⟹ 2/10
⟹ 0.2

Option (c) is the right answer

(02) Calculate the decimal for below grid diagram

(a) 0.5
(b) 0.7
(c) 1.2
(d) 0.9

Total number of box = 10
Number of colored box = 5

Colored Box Fraction:
⟹ 5/10
⟹ 0.5

Option (a) is the solution

(03) Find the fraction of colored boxes in given grid

(a) 0.3
(b) 1.2
(c) 1.3
(d) 2.3

Box 01
Total number of box = 10
Number of colored box = 10

Fraction for Box 1
⟹ 10/10
⟹ 1

Box 02
Total number of Box = 10
Number of colored box = 3

Fraction for Box 2
⟹ 3/10
⟹ 0.3

Total Fraction for Grid
⟹ 1 + 0.3
⟹ 1.3

Option (c) is the right answer

(04) Find the decimal of the given diagram

(a) 0.7
(b) 1.7
(c) 1.8
(d) 2.8

Box 01
Total number of box = 10
Number of colored box = 10

Fraction for Box 1
⟹ 10/10
⟹ 1

Box 02
Total number of Box = 10
Number of colored box = 7

Fraction for Box 2
⟹ 7/10
⟹ 0.7

Fraction for Total Grid
⟹ 1 + 0.7
⟹ 1.7

Option (b) is the right answer

(05) Find the decimal of below diagram

(a) 2.1
(b) 1.1
(c) 1.5
(d) 2.7

Solution
Fraction for Box 1 ⟹ 10/10 ⟹ 1

Fraction for Box 2 ⟹ 10/10 ⟹ 1

Fraction for Box 3 ⟹ 1/10 ⟹ 0.1

Total Fraction
⟹ 1 + 1 + 0.1
⟹ 2.1

Option (a) is the right answer

(06) Find the decimal of the below colored box

(a) 0.17
(b) 0.12
(c) 1.12
(d) 0.13

Total number of box = 100
Colored box = 12

Fraction of colored box
⟹12/100
⟹ 0.12

Option (b) is the right answer

(07) Find the decimal of the given box

(a) 0.26
(b) 0.24
(c) 1.15
(d) 0.26

Total number of box = 100
Colored box = 26

Fraction of colored box
⟹26/100
⟹ 0.26

Option (d) is he right answer

(08) Find the decimal for below image

(a) 1.26
(b) 1.33
(c) 1.30
(d) 2.24

Fraction for 1st Box = 1

Fraction for 2nd Box ⟹ 33/100 ⟹0.33

Total fraction of image
⟹ 1+ 0.33
⟹ 1.33

Option (b) is the solution