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:
1^{st} way: 4 ten thousands + 3 thousands + 2 hundreds + 5 tens + 7 ones
2^{nd} way: 4 × 10000 + 3 × 1000 + 2 × 100 + 5 × 10 + 7 × 1
3^{rd} 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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