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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 standard form
  2. 68 030 484 standard form
  3. 20 202 202 standard form
  4. 730 284 069 standard form
  5. 900 900 909 standard form
  6. 40 000 017 standard form

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:

Place value 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

Place value

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

standard form

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

standard form

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

standard form

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

Related Tags

What is an Expanded Notation?, Examples on Expanded Notation