Expanded form of a Number
We know that the number written as sum of the place-values of its digits is called the expanded form of a number.
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Standard Form
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Expanded Form
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20,37,81,405
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=
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20,00,00,000 + 0 + 30,00,000 + 7,00,000 + 80,000 + 1,000 + 400 + 0 + 5
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In expanded form of a number, the number is shown according to the place values of its digits.
This is shown here:
In 2385, the place values of the digits are given below:
Hence, 2385 = 2000 + 300 + 80 + 5
Thus, 2000 + 300 + 80 + 5 is the expanded form of 2385.
Again,
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2,55,109
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=
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2,00,000 + 50,000 + 5,000 + 100 + 0 + 9
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Standard Form
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Expanded Form
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Solved Examples on Expanded Form of a Number:
1. Write the expanded form for the number 70,39,41,295.
Solution:
Therefore, the expanded form of the number 70,39,41,295 is 70,00,00,000 + 00000000 + 3000000+ 900000 + 40000 + 1000 + 200 + 90 + 5.
2. Find the expanded form of 453169.
Solution:
Place values of digits 453169
So, 453169 = 400000 + 50000 + 3000 + 100 + 60 + 9
3. Write the number in figures and then in words for the following expanded form:
(i) 80000 + 8000 + 500 + 50 + 7
Solution:
80000 + 8000 + 500 + 50 + 7
= 88557 (in figures)
Eighty eight thousand five hundred fifty seven (in words)
(ii) 100000 + 30000 + 2000 + 10 + 6
Solution:
100000 + 30000 + 2000 + 10 + 6 = 132016 (in figures)
One hundred thirty two thousand sixteen (in words)
We can write the expanded form of numbers in different ways.
4. Write in expanded form:
(i) 28369
Write as:
(a) 20000 + 8000 + 300 + 60 + 9
(b) 2 × 10000 + 8 × 1000 + 3 × 100 + 6 × 10 + 9 × 1
(c) 2 ten thousands + 8 thousands + 3 hundreds + 6 tens + 9 ones
(ii) 419,247
Write as:
(a) 400000 + 10000 + 9000 + 200 + 40 + 7
(b) 4 × 100000 + 1 × 10000 + 9 × 1000 + 2 × 100 + 4 × 10 + 7 × 1
(c) 4 hundred thousands + 1 ten thousands + 9 thousands + 2 hundreds + 4 tens + 7 ones
Questions and Answers on Expanded Form of a Number:
I. Write the expanded form for the
given numbers:
(i) 7,12,306
(ii) 8,07,392
(iii) 6,44,895
(iv) 3,73,737
(v) 9,22,005
Answers:
(i) 7,00,000 + 10,000 + 2,000 + 300 + 0 + 6
(ii) 8,00,000 + 0 + 7,000 + 300 + 90 + 2
(iii) 6,00,000 + 40,000 + 4,000 + 800 + 90 + 5
(iv) 3,00,000 + 70,000 + 3,000 + 700 + 30 + 7
(v) 9,00,000 + 20,000 + 2,000 + 0 + 0 + 5
II. Write
the given number in standard form:
(i) 30,000
+ 4,000 + 700 + 2
(ii) 2,00,000
+ 80,000 + 4,000 + 800 + 50
(iii) 6,00,000
+ 40,000 + 4,000 + 800 + 90 + 5
(iv) 8,00,000
+ 10,000 + 6,000 + 200 + 50 + 7
(v) 1,00,000
+ 20,000 + 1,000 + 200 + 10 + 2
(vi) 9,00,000
+ 2
Answers:
(i) 34702
(ii) 2,84,850
(iii) 6,44,895
(iv) 8,16,257
(v) 1,21,212
(vi) 9,00,002
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