Expanded Form and Short Form of a Number

When we write a number as a sum of place value of its digits, the number is said to be in expended form and when we write a number using digits, the number is said to be in short form.


Expanded Form of a Number:

When we write 3476, the number really means 3000 + 400 + 70 + 6. This means we have expanded the number to show the value of each of its digit.

The expanded form of a number is the method of expressing the number as the sum of the place value of all its digits.

For example,

Consider the number 2815

2815 = 2000 + 800 + 10 + 5

There are 3 ways to write the expanded form. There are 3 ways to write the expanded form for a given number.


Examples on Expanded Form of a Number:

1. Write the expanded form for 43,257.

Solution:

1st way: 4 ten thousands + 3 thousands + 2 hundreds + 5 tens + 7 ones

2nd way: 4 × 10000 + 3 × 1000 + 2 × 100 + 5 × 10 + 7 × 1

3rd way: 40000 + 3000 + 200 + 50 + 7

2. Write the expanded form for 14,080.

Solution:

14,080 = 1 ten thousand + 4 thousands + 8 tens   [Note: We do not write the place value for hundreds and ones as these places are filled with zero.]

or, 1 × 10000 + 4 × 1000 + 8 × 10

or, 10000 + 4000 + 80


Standard Form of a Number / Short Form of a Number:

The standard form of a number is a way of expressing the expanded form in figures.

For example, the standard form of 7000 + 400 + 10 + 1 = 7411


Examples on Expanded Form and Short Form of a Number:

3. Write the short form for the given expanded forms.

(i) 8 ten thousands + 6 hundreds + 6 tens + 3 ones

(ii) 9  × 10000 + 7 × 1000 + 4 × 10 + 2

(iii) 40000 + 3000 + 900 + 70 + 8

Solution:

                 Expanded Form

(i) 8 ten thousands + 6 hundreds + 6 tens + 3 ones

(ii) 9 × 10000 + 7 × 1000 + 4 × 10 + 2

(iii) 40000 + 3000 + 900 + 70 + 8

Short Form

80663

97042

43978


Questions and Answers on Expanded Form and Standard Form of a Number:

I. Write in the expanded form:

(i) 5896

(ii) 3817

(iii) 6399

(iv) 1357

(v) 3434

(vi) 5690


Answer:

I. (i) 5000 + 800 + 90 + 6

(ii) 3000 + 800 + 10 + 7

(iii) 6000 + 300 + 90 + 9

(iv) 1000 + 300 + 50 + 7

(v) 3000 + 400 + 30 + 4

(vi) 5000 + 600 + 90 + 0



II. Write in the standard form:

(i) 2000 + 900 + 90 + 9

(ii) 8000 + 200 + 50 + 3

(iii) 1000 + 400 + 50 + 2

(iv) 4000 + 300 + 9

(v) 6000 + 900 + 80 + 4


Answer:

II. (i) 2999

(ii) 8253

(iii) 1452

(iv) 4309

(v) 6984

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