In this post we will learn the concept of expansion of numbers with decimals.

After learning the concept we will move to solve questions related to this chapter.

In order to understand the concept of number expansion you should have clear idea of place values of numbers.

**Expanded form Math**

In number expansion we basically show that any given number is made of sum of individual digits.

In order to expand any given number, we do following steps:

(a) Find the Place value of individual digits of number

(b) Multiply the digits with its factor place value

(c) Adding all the digits to form the number

Let us understand the above steps with the help of example.

First let us start with the simple whole number.

**Example 01**

write number 1279 in expanded form

Solution

Do the following steps for number expansion

**(a) Find Place value of all given numbers**

Here we will take help of Place Value chart

From the above table you can note that:

1 ⟹ is in Thousand Place

2 ⟹ is in Hundred Place

7 ⟹ is in Tens Place

9 ⟹ is in Ones Place

**(b) Multiply each digit with place value**

⟹ 1 x 1000 = 1000

⟹ 2 x 100 = 200

⟹ 7 x 10 = 70

⟹ 9 x 1 = 9

(c) **Add all the individual digits**

1279 ⟹**1000 + 200 + 70 + 9**

Hence the expanded form of 1279 is ⟹ **1000 + 200 + 70 + 9**

I hope the concept of number expansion is clear till now.

Let us now introduce decimal numbers for number expansion.

**Example 02**

Write number 32.587 in expanded form

**Solution**Follow the below steps

**Steps 01**

Write the place value of all the individual digits

Below is the place value chart for identification of place value

From the above table we can note that

3 ⟹ is in Tens Place

2 ⟹ is in Ones Place

. ⟹ is decimal point

5 ⟹ is in tenth place

8 ⟹ is in Hundredth Place

7 ⟹ is in Thousandth Place

**Step 02**

Multiply the digits with place value

⟹ 3 x 10 = 30

⟹ 2 x 1 = 2

⟹ 5 x \frac{1}{10} = \frac{5}{10}\\\ \\

⟹ 8 x \frac{1}{100} = \frac{8}{100} \\\ \\

⟹ 7 x \frac{1}{1000} = \frac{7}{1000} \\\ \\

**Step 03**

Add all the individual digits

32.587 ⟹ 30 + 2 + \frac{5}{10} + \frac{8}{100} + \frac{7}{1000}\\\ \\

**Example 03**

Write number 4001.205 in expanded form

Follow the below steps**Step 01**

Find the place value of all the digits

We will take the help of Place Value chart

From the above chart, we note that:

4 ⟹ is in Thousands Place

0 ⟹ is in Hundreds Place

0 ⟹ is in Tens Place

1 ⟹ is in Ones Place

. ⟹ is decimal point

2 ⟹ is in tenth place

0 ⟹ is in Hundredth Place

5 ⟹ is in Thousandth Place

**Step 02**

Multiply the digits with the place values

⟹ 4 x 1000 = 4000

⟹ 0 x 100 = 0

⟹ 0 x 10 = 0

⟹ 1 x 1 = 1

⟹ 2 x \frac{1}{10} = \frac{2}{10}

⟹ 0 x \frac{1}{100} = \frac{0}{100} = 0

⟹ 5 x \frac{1}{1000} = \frac{5}{1000}

**Step 03**

Add all the individual digits

4001.205 = 4000 + 0 + 0 + 1 + \frac{2}{10} + 0 + \frac{5}{1000}

I hope the concept of number expansion is clear till now.

Let’s move on to solve some practice exercise

**Number Expansion Worksheet**

In this section we will solve questions related to number expansion of decimal numbers.

All questions are to the standard of Grade 5.

Each questions are provided with detailed solution

**Write the numbers in Expanded form **

Here decimal numbers are provided in each question.

You have to present the numbers in expanded form.

(a) **7833.39**

Find Place Value of Individual digits

From the table you can see that

7 ⟹ is in Thousands Place

8 ⟹ is in Hundreds Place

3 ⟹ is in Tens Place

3 ⟹ is in Ones Place

. ⟹ is decimal point

3 ⟹ is in tenth place

9 ⟹ is in Hundredth Place

5 ⟹ is in Thousandth Place

So the expanded form of number can be written as:

⟹ 7 Thousands + 8 hundred + 3 Tens + 3 Ones + 3 Tenths + 9 Hundredths + 5 Thousandth

⟹ 7000 + 800 + 30 + 3 + (3/10) + (9/100) + (5/1000)

(b) **653.7**

The expanded for of 653.7 can be written as:

⟹ 6 hundred + 5 Tens + 3 Ones + 7 Tenth

⟹ 600 + 50 + 3 + (7/10)

(c) **3.602**

The number 3.602 can be expanded as

⟹ 3 ones + 6 Tenth + 0 hundredth + 2 Thousandth

⟹ 3 + (6/10) + (0/100) + (2/1000)

⟹ 3 + (6/10) + (2/1000)

(d) **42.71**

The number 42.71 can be expressed as:

⟹ 4 Tens + 2 ones + 7 Tenth + 1 hundredth

⟹ 40 + 2 + (7/10) + (1/100)

(e) **1025.253**

The number 42.71 can be expressed as:

⟹ 1 Thousands + 0 Hundreds+ 2 Tens + 5 ones + 2 Tenth + 5 hundredth + 1 Thousandth

⟹ 1000 + 0 + 20 + 5 + (2/10) + (5/100) + (1/1000)

(f) **374.69**

The number 374.69 can be expressed as:

⟹ 3 Hundreds+ 7 Tens + 4 ones + 6 Tenth + 9 hundredth

⟹ 300 + 70 + 4 + (6/10) + (9/100)

(g)** 1.735**

The number 1.735 can be expressed as:

⟹ 1 ones + 7 Tenth + 3 hundredth + 5 Thousandth

⟹ 1 + (7/10) + (3/100) + (1/1000)

**(h) 0.2**

The number 0.2 can be expressed as:

⟹ 0 ones + 2 Tenth

⟹ 0 + (2/10)

(i) **63.251**

The number 63.251 can be expressed as:

⟹ 6 Tens + 3 ones + 2 Tenth + 5 hundredth + 1 Thousandth

⟹ 60 + 3 + (2/10) + (5/100) + (1/1000)

(j) **0.301**

The number 0.301 can be expressed as:

⟹ 0 ones + 3 Tenth + 0 hundredth + 1 Thousandth

⟹ 0 + (3/10) + (0/100) + (1/1000)

⟹ (3/10) + (1/1000)

**Write the decimals for given expanded numbers**

Here expanded numbers are provided in the question.

You have to understand the number and write in decimal form

(1) 7 Hundreds + 4 Tens + 2 Ones + 5 Tenths

(a) 763.2

(b) 845.3

(c) 740.2

(d) 742.5

Read Solution

The expanded numbers can be written as:

⟹ 700 + 40 + 2 + (5/10)

⟹742 + 0.5

⟹ 742.5

Hence 742.5 is the solution

**Option (d) is the right answer**

(02) 1 Thousands + 1 Tens + 3 Ones + 6 Tenths + 2 Hundredths

(a) 1013.4

(b) 1013.62

(c) 1013.6

(d) 1013.63

⟹ 1000 + 10 + 3 + (6/10) + (2/100)

⟹ 1013 + 0.6 + 0.02

⟹ 1013.62

**Option (b) is the right answer**

(03) 2 Tens + 4 Ones + 8 Tenths + 6 Hundredths + 9 Thousandth

(a) 24.869

(b) 24.991

(c) 24.842

(d) 24.356

⟹ 20 + 4 + (8/10) + (6/100) + (9/1000)

⟹ 24 + 0.8 + 0.06 + 0.009

⟹ 24.869

**Option (a) is the right answer**

(04) 1 Hundreds + 5 Tenths + 2 Hundredths

(a) 100.55

(b) 101.55

(c) 101.52

(d) 100.52

⟹ 100 + (5/10) + (2/100)

⟹ 100 + 0.5 + 0.02

⟹ 100.52

**Option (d) is the right answer**

(05) 2 Hundreds+ 2 Tens + 2 ones + 2 Tenth + 2 hundredth + 2 Thousandth

(a) 333.222

(b) 222.333

(c) 222.222

(d) 222.232

⟹ 200 + 20 + 2 + (2/10) + (2/100) + (2/1000)

⟹ 222 + 0.2 + 0.02 + 0.002

⟹ 222.222

**Option (c) is the right answer**

(06) 2 Tens + 4 ones + 3 Tenth + 6 Thousandth

(a) 24.306

(b) 24.97

(c) 24.303

(d) 24.31

⟹ 20 + 4 + (3/10) + (6/1000)

⟹ 24 + 0.3 + 0.006

⟹ 24.306

**Option (a) is the right answer**

(07) 8 thousands + 5 Tens + 2 ones + 3 Tenth + 7 hundredth + 1 Thousandth

(a) 8051.220

(b) 8052.120

(c) 8052.371

(d) 8051.330

⟹ 8000 + 50 + 2 + (3/10) + (7/100) + (1/1000)

⟹ 8052 + 0.3 + 0.07 + 0.001

⟹ 8052.371

**Option (c) is the right answer**

(08) 1 Tenth + 9 Thousandth

(a) 0.109

(b) 0.207

(c) 0.110

(d) 0.190

⟹ (1/10) + (9/1000)

⟹ 0.1 + 0.009

⟹ 0.109

**Option (a) is the right answer**

(09) 9 Tens + 9 ones + 6 Tenth + 1 hundredth

(a) 99.66

(b) 99.61

(c) 99.16

(d) 99.69

⟹ 90 + 9 + (6/10) + (1/100)

⟹ 99 + 0.6 + 0.01

⟹ 99.61

**Option (b) is the right answer**

(10) 4 Tenth + 5 Hundredth + 2 Thousandth

(a) 0.456

(b) 0.472

(c) 0.551

(d) 0.452

⟹ (4/10) + (5/100) + (2/1000)

⟹ 0.4 + 0.05 + 0.002

⟹ 0.452

**Option (d) is the right answer**