Use of Commas

In Mathematics, we learn “Use of Commas” when the numbers are large. When we write or read large numbers, then commas are used. But we do not use commas while writing the names of numbers. As per the Indian System of Numeration, commas are used based on ones, tens, hundreds, thousands and then lakhs and crores. For example, one lakh is represented as 1,00,000.

In the same way, there are many examples of large numbers in real life such as the population of India, RBC and WBC counts in the human body, etc., which can be written properly using commas.

Also read: Playing with Numbers

Rules for Using Commas

There are certain rules for using commas between the digits of large numbers. Let us see what are these rules:

• For a large number, the first comma has to be placed after hundreds place (that means three digits from the right of the given number). This comma marks thousands.
• The second comma will come after the next two digits (that means five digits from the right of the given number). This comma comes past ten thousand places and marks lakh.
• The third comma will come after the next two digits (that means seven digits from the right of the given number).This comma comes after ten lakh places and marks crore.

In the international system of numeration, the commas are used in a different way.

• The order of using commas will be ones, tens, hundreds, thousands and then millions.
• Since, we know, one million is equal to ten lakhs or thousand thousands. Therefore, the commas are used to mark thousands and millions.
• If we go further million counts, then 1000 millions is equal to 1 billion

For example, 50,908,234 is fifty million nine hundred eight thousand two hundred and thirty-four, but in the Indian system it will be five crore eight lakh eight thousand two hundred thirty four.

To make it easy to compare the numbers in the indian and international system, read the points below.

• 100 thousand = 1 lakh
• 1 million = 10 lakhs
• 10 millions = 1 crore
• 100 millions= 10 crores

Solved Examples

Q.1: Write the given numbers using commas in Indian and international system of numeration.

• 5274859
• 86953
• 84924030
• 770010

Solution:

For 5274859,

• Indian Numeration = 52,74,859
• International Numeration = 5,274,859

For 86953,

• Indian Numeration = 86,953
• International Numeration = 86,953

For 84924030,

• Indian Numeration = 8,49,24,030
• International Numeration = 84,924,030

For 770010,

• Indian Numeration = 7,70,010
• International Numeration = 770,010

Q.2: Place the commas correctly and write the numbers.

• Eighty three lakh seventy five thousand three hundred seven.
• Nine crore fifty two lakh twenty one thousand three hundred two.
• Thirty three lakh thirty thousand ten.

Solution:

• Eighty three lakh seventy five thousand three hundred seven – 83,75,307
• Nine crore fifty two lakh twenty one thousand three hundred two – 9,52,21,302
• Thirty three lakh thirty thousand ten – 33,30,010

Q.3: Write the below number names in numeral form.

(a) Forty two lakh seventy thousand eight.

(b) Two crore ninety lakh fifty five thousand eight hundred.

(c) Seven crore sixty thousand fifty five.

Solution:

(a) Forty two lakh seventy thousand eight – 42,70,008

(b) Two crore ninety lakh fifty five thousand eight hundred – 2,90,55,800

(c) Seven crore sixty thousand fifty five – 7,00,60,055

Q.4: Write the given numbers using commas and in the expanded form.

(i) 475320

(ii) 9847215

(iii) 97645310

(iv) 30458094

Solution:

(i) 475320

Using commas → 4,75,320

Expanded form → 4 x 100000 + 7 x 10000 + 5 x 1000 + 3 x 100 + 2 x 10 + 0

(ii) 9847215

Using commas → 98,47,215

Expanded form → 9 x 1000000 + 8 x 100000 + 4 x 10000 + 7 x 1000 + 2 x 100 + 1 x 10 + 5

(iii) 97645310

Using commas → 9,76,45,310

Expanded Form → 9 x 10000000 + 7 x 1000000 + 6 x 100000 + 4 x 10000 + 5 x 1000 + 3 x 100 + 1 x 10 + 0

(iv) 30458094

Using commas → 3,04,58,094

Expanded form → 3 x 10000000 + 0 + 4 x 100000 + 5 x 10000 + 8 x 1000 + 0 + 9 x 10 + 4