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# Expanded Notation

The way we write the numericals in general is called as standard notation.

## Examples of Standard Form

Example: Write the following numbers in standard notation:

1. 3 000 000+ 700 000+ 60 000+ 9 000+ 70+ 6
2. 60 000 000+ 8000000+ 30 000+ 400+ 80+ 4
3. 200 000 00+ 200 000 + 2 000+ 2 002
4. 700 000 000+ 30 000 000+ 200 000+ 80 000+ 4 000+ 60+ 9
5. 900 000 000+ 900 000+ 900+9
6. 40 000 000+ 10+ 7

Solution: The standard notation of these numbers will be as follows:

1. 3 769 076
2. 68 030 484
3. 20 202 202
4. 730 284 069
5. 900 900 909
6. 40 000 017

## Expanded Form

Expanded form is a manner of writting the numbers as the sum of digits so that each digit represents its place value.

## Examples of Expanded Form

Example: Write 490 570 316 in the expanded form.

Solution: The given numerical may be written as:

Thus, we have:

490 670 316

= 4 ten-crores + 9 crores + 0 ten-lakhs + 5 lakhs+ 7 ten- thousands + 0 thousand + 2 hundreds + 1 ten + 6 ones

= 4 x 100000000 + 9 x 10000000 + 0 x 1000000 + 5 x 100000 + 7 x 10000 + 0 x 1000 + 3 x 100 + 1 x 10 + 6 x 1.

= 400000000 + 90000000 + 0 + 500000 + 70000 + 0 + 300 + 10 +6

= 400000000 + 90000000 + 500000 + 70000 + 300 + 10 + 6

Example: write 5,29,347 in expanded form.

Solution: the given numerical may be written as

Thus, we have

529347

= 5 lakhs + 2 ten-thousand + 9 thousands + 3 hundreds + 4 tens + 7 ones

= 5 x 100000 + 2 x 10000 + 9 x 1000 + 3x 100 + 4 x 10 + 7

= 500000 + 20000 + 9000 + 300 + 40 + 7

Example: write 23,09,519 in expanded form.

Solution: the given numerical may be written as

Thus, we have

2309519

= 2 ten-lakhs + 3 lakhs + 0 ten- thousands + 9 thousand + 5 hundred +1 ten + 9 ones

= 2 x 1000000 + 3 x 100000 + 0 x 10000 + 9 x 1000 + 5 x 100 + 1 x 10 + 9 x 1

= 2000000 + 300000 +0 + 9000 + 500 + 10 + 1

= 2000000 + 300000 + 9000 + 500 + 10 + 1

Example: write 9,72,34,026 in expanded form.

Solution: The given numerical may be written as

Thus, we have

97234026

=9 crore + 7 ten-lakhs +2 lakh + 3 ten thousand + 4 thousand + 0 hundreds + 2 tens + 6 ones.

=9 x 10000000 + 7 x 1000000 + 2x 100000 + 3 x 10000 + 4 x 1000+ 0 x 100 + 2 x 10 + 6 x 1

= 90000000 + 7000000 + 200000 + 3 x 10000 + 4000 + 0 + 20 + 6

= 90000000 + 7000000 + 200000 + 30000 + 4000 + 20 + 6

Example: Example: write 893016870 in expanded form.

Solution: The given numerical may be written as

Thus, we have

893016870

= 8 Ten-crore + 9 crore + 3 ten-lakh + 0 lakhs + 1 ten-thousands + 6 thousand + 8 hundred + 7 tens + 0 ones

= 8 x 100000000 + 9 x 10000000 + 3 x 1000000 + 0 x 100000 + 1 x 10000 + 6 x 1000 + 8 x 100 + 7 x 10 + 0 x 1

= 800000000 + 90000000 + 3000000 +0 + 10000 + 6000 + 800 + 70 + 0

= 800000000 + 90000000 + 3000000 + 10000 + 6000 + 800 + 70