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We all know that the quantity written as sum of the place-values of its digits is known as the expanded type of a quantity.
|
Customary Type |
Expanded Type |
|
|
20,37,81,405 |
= |
20,00,00,000 + 0 + 30,00,000 + 7,00,000 + 80,000 + 1,000 + 400 + 0 + 5 |
In expanded type of a quantity, the quantity is proven in line with the place values of its digits.
That is proven right here:
In 2385, the place values of the digits are given under:
Therefore, 2385 = 2000 + 300 + 80 + 5
Thus, 2000 + 300 + 80 + 5 is the expanded type of 2385.
Once more,
|
2,55,109 |
= |
2,00,000 + 50,000 + 5,000 + 100 + 0 + 9 |
|
Customary Type |
Expanded Type |
Expanded
Notation
The digits of the numerals 394381, 163845, 583927 are
entered within the place worth chart as given under.
|
Lakhs 100000 |
Ten hundreds 10000 |
Hundreds 1000 |
A whole lot 100 |
Tens 10 |
Ones 1 |
|
3 |
9 |
4 |
3 |
8 |
1 |
|
1 |
6 |
3 |
8 |
4 |
5 |
|
5 |
8 |
3 |
9 |
2 |
7 |
(i) What’s the expanded type of the quantity 394381?
394381 =
3 lakhs + 9 ten hundreds + 4 hundreds + 3 a whole lot +
8 tens + 1 one
=
3 × 100000 + 9 × 10000 + 4 × 1000 + 3 × 100 + 8 × 10 +
1 × 1
=
300000 + 90000 + 4000 + 300 + 80 + 1
(ii) What’s the expanded type of the quantity 163845?
163845 =
1 lakhs + 6 ten hundreds + 3 hundreds + 8 a whole lot +
4 tens + 5 ones
=
1 × 100000 + 6 × 10000 + 3 × 1000 + 8 × 100 + 4 × 10 +
= 5 × 1
=
100000 + 60000 + 3000 + 800 + 40 + 5
(iii) What’s the place worth of all of the digits of quantity 583927?
|
Digit |
Place Worth |
||
|
5 |
5 |
→ |
5 × 100000 = 500000 |
|
8 |
8 |
→ |
8 × 10000 = 80000 |
|
3 |
3 |
→ |
3 × |
|
9 |
9 |
→ |
9 × |
|
2 |
2 |
→ |
2 × |
|
7 |
7 |
→ |
7 × |
Given the expanded type of a quantity, we are able to additionally write the
numeral in the usual type.
500000 + 80000 + 3000 + 900 + 20 + 7
= 583927
Expanded type of a quantity to plain type.
(iv) 3000 + 200 + 40 + 8 = 3248
(v) 7 ten hundreds + 4 hundreds + 2 a whole lot + 3 tens + 8 ones
= 74238
Solved Examples on Expanded Type of a Quantity:
1. Write the expanded type for the quantity 70,39,41,295.
Resolution:
Due to this fact, the expanded type of the quantity 70,39,41,295 is 70,00,00,000 + 00000000 + 3000000+ 900000 + 40000 + 1000 + 200 + 90 + 5.
2. Discover the expanded type of 453169.
Resolution:
Place values of digits 453169
So, 453169 = 400000 + 50000 + 3000 + 100 + 60 + 9
3. Write the quantity in figures after which in phrases for the next expanded type:
(i) 80000 + 8000 + 500 + 50 + 7
Resolution:
80000 + 8000 + 500 + 50 + 7
= 88557 (in figures)
Eighty eight thousand 5 hundred fifty seven (in phrases)
(ii) 100000 + 30000 + 2000 + 10 + 6
Resolution:
100000 + 30000 + 2000 + 10 + 6 = 132016 (in figures)
100 thirty two thousand sixteen (in phrases)
We are able to write the expanded type of numbers in numerous methods.
4. Write in expanded type:
(i) 28369
Write as:
(a) 20000 + 8000 + 300 + 60 + 9
(b) 2 × 10000 + 8 × 1000 + 3 × 100 + 6 × 10 + 9 × 1
(c) 2 ten hundreds + 8 hundreds + 3 a whole lot + 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 hundreds + 1 ten hundreds + 9 hundreds + 2 a whole lot + 4 tens + 7 ones
Numbers Past One Lakh
|
1 2 lakhs 3 lakhs 4 lakhs 5 lakhs 6 lakhs 7 lakhs 8 lakhs 9 lakhs 10 lakhs |
= 10(^{5}) = 2 × 10(^{5}) = 3 × 10(^{5}) = 4 × 10(^{5}) = 5 × 10(^{5}) = 6 × 10(^{5}) = 7 × 10(^{5}) = 8 × 10(^{5}) = 9 × 10(^{5}) = 10 × 10(^{5}) |
= 100000 = 200000 = 300000 = 400000 = 500000 = 600000 = 700000 = 800000 = 900000 = 1000000 |
Observe: There are 7 digits in ten lakhs.
Due to this fact the seventh place is known as ten lakhs place.
Questions and Solutions on Expanded Type of a Quantity:
I. Write the given numbers in expanded type:
(i) 617 = _____ + _____ + _____
(ii) 319 = _____ + _____ + _____
(iii) 286 = _____ + _____ + _____
(iv) 939 = _____ + _____ + _____
(v) 677 = _____ + _____ + _____
(vi) 918 = _____ + _____ + _____
(vii) 328 = _____ + _____ + _____
(viii) 520 = _____ + _____ + _____
(ix) 647 = _____ + _____ + _____
(x) 474 = _____ + _____ + _____
Reply:
I. (i) 600 + 10 + 7
(ii) 300 + 10 + 9
(iii) 200 + 80 + 6
(iv) 900 + 30 + 9
(v) 600 + 70 + 7
(vi) 900 + 10 + 8
(vii) 300 + 20 + 8
(viii) 500 + 20 + 0
(ix) 600 + 40 + 7
(x) 400 + 70 + 4
II. Write the expanded type for the given numbers:
(i) 7,12,306
(ii) 8,07,392
(iii) 6,44,895
(iv) 3,73,737
(v) 9,22,005
Solutions:
II. (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
III. Write the given quantity in customary type:
(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
Solutions:
III. (i) 34702
(ii) 2,84,850
(iii) 6,44,895
(iv) 8,16,257
(v) 1,21,212
(vi) 9,00,002
IV. Rearrange and write the quantity:
|
(i) 5 ones 6 tens 1 hundred (ii) 7 a whole lot 9 ones 1 ten (iii) 3 tens 5 a whole lot 6 ones (iv) 8 ones 9 tens 2 a whole lot (v) 4 a whole lot 6 ones 7 tens (vi) 2 tens 3 a whole lot 6 ones |
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ |
Reply:
|
(i) 1 hundred 6 tens 5 ones (ii) 7 a whole lot 1 ten 9 ones (iii) 5 a whole lot 3 tens 6 ones (iv) 2 a whole lot 9 tens 8 ones (v) 4 a whole lot 7 tens 6 ones (vi) 3 a whole lot 2 tens 6 ones |
= = = = = = |
165 719 536 298 476 326 |
V. Circle the proper one
|
(i) 9 a whole lot 2 tens 3 ones (ii) 6 a whole lot 0 tens 1 one (iii) 3 a whole lot 6 tens 3 ones (iv) 2 a whole lot 2 tens 1 one (v) 5 a whole lot 8 tens 4 ones (vi) 9 a whole lot 8 tens 0 ones |
932 923 329 106 601 610 363 336 633 212 221 122 854 584 485 980 908 809 |
Reply:
(i) 923
(ii) 601
(iii) 363
(iv) 221
(v) 584
(vi) 980
VI. Write the next numbers within the expanded type in three
other ways as proven within the examples.
(i) 61,052
61,052 – 6 ten hundreds + 1 thousand + 0
a whole lot + 5 tens + 2 ones
– 6 ×
10000 + 1 × 1000 + 0 × 100 + 5 × 10 + 2× 1
– 60000
+ 1000 + 0 + 50 + 2
(ii) 1, 99, 099
(iii) 2,80,476
(iv) 3,67,814
(v) 8,31, 879
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