Selina Concise Solutions for ICSE Class 6 Mathematics Chapter 3 Numbers in India and International System

Important Points

1. Place Value (Local Value): This is the value of a digit based on where it sits in a number.
For example, in the number 6453:
- The place value of 6 is 6 thousands = \( 6 \times 1000 = 6000 \)
- The place value of 4 is 4 hundreds = \( 4 \times 100 = 400 \)
- The place value of 5 is 5 tens = \( 5 \times 10 = 50 \)
- The place value of 3 is 3 ones = \( 3 \times 1 = 3 \)

2. Face Value (True Value): This is the actual value of a digit itself. It does not change no matter where the digit is in the number.
For example, in the same number 6453:
- The face value of 6 is 6.
- The face value of 4 is 4.
- The face value of 5 is 5.
- The face value of 3 is 3.

3. An Abstract Number: This is a number that does not talk about any real objects or units. Examples are 3, 5, and 9.

4. A Concrete Number: This is a number that describes real things or units. Examples are 3 boys, 5 girls, or 9 rooms.

The smallest single-digit number is 1.

The biggest single-digit number is 9.

Exercise 3

Question 1. Write the following numerals using Indian System words or International system (as required in words) :
(i) 4, 35, 342 = …………..
(ii) 36, 71, 430 = …………..
(iii) 4, 28, 30, 004 = …………..
(iv) 75, 132, 684 = ……………
(v) 815, 906 = …………….
(vi) 5, 420, 700 = ……………..
Answer:
(i) Four lakh, thirty-five thousand, three hundred forty-two
(ii) Thirty-six lakh, seventy-one thousand, four hundred thirty
(iii) Four crore, twenty-eight lakh, thirty thousand four
(iv) Seventy-five million, one hundred thirty-two thousand, six hundred eighty-four
(v) Eight hundred fifteen thousand, nine hundred six
(vi) Five million, four hundred twenty thousand, seven hundred
In simple words: Look at the commas to find which system to use. If the commas group digits by twos, use Indian lakhs and crores. If they group by threes, use International millions and thousands.

Exam Tip: Remember that "lakh" and "crore" belong to the Indian system, while "million" belongs to the International system. Do not mix them up in the same answer.

Question 2. Write the following numbers, placing the commas, according to Indian system :
(i) 835629 = …………
(ii) 35640254 = …………
(iii) 2826040 = ………
Answer:
(i) 8,35,629
(ii) 3,56,40,254
(iii) 28,26,040
In simple words: In the Indian system, you must group the digits. Put the first comma after the hundreds place (three digits from the right), and then put commas after every two digits as you move left.

Exam Tip: When writing numbers in the Indian system, commas go after the 3rd, 5th, and 7th digits starting from the right side.

Question 3. Write the following numbers, by placing the commas, according to International system :
(i) 6509820 = ………..
(ii) 428140584 = …………
(iii) 63560981 = ……….
Answer:
(i) 6,509,820
(ii) 428,140,584
(iii) 63,560,981
In simple words: For the International system, group the numbers by threes. Put a comma after every three digits starting from the right.

Exam Tip: In the International system, every comma is placed after exactly three digits. Never leave a group of two digits in the middle.

Question 4. Fill in the blanks :
(i) Four lakh sixty seven thousand three hundred six.
= ……………… (In numeral form)
= …………… (In International System)
= ……………. (In International numeration)
(ii) Thirteen lakh forty five.
= ……………. (In numeral form)
= ……………. (In International System)
= ……………. (In International numerals)
Answer:
(i) Four lakh sixty-seven thousand three hundred six:
= 4,67,306 (In numeral form)
= 467,306 (In International System)
= Four hundred sixty-seven thousand three hundred six (In International numeration)

(ii) Thirteen lakh forty-five:
= 13,00,045 (In numeral form)
= 1,300,045 (In International System)
= One million three hundred thousand forty-five (In International numerals)
In simple words: Change the written-out number into standard digits. Then, move the commas to switch between the Indian system and the International system, and write the new word name.

Exam Tip: Be extra careful with zeros as placeholders when writing numbers. For "Thirteen lakh forty-five", you need to fill the ten-thousands, thousands, and hundreds places with zeros to get 13,00,045.

Question 5. Fill in the blanks :
(i) Six hundred four thousand eight hundred forty seven.
= ……………. (In numeral form)
= ……………. (In Indian System)
= ……………… (Number name in Indian System)
(ii) Two million three hundred ten thousand one hundred four
= …………….. (In numeral form)
= …………… (In Indian System)
= ……………. (In Indian numeration)
= …………….. (In international numerals)
Answer:
(i) Six hundred four thousand eight hundred forty-seven:
= 604,847 (In numeral form)
= 6,04,847 (In Indian System)
= Six lakh four thousand eight hundred forty-seven (Number name in Indian System)

(ii) Two million three hundred ten thousand one hundred four:
= 2,310,104 (In numeral form)
= 23,10,104 (In Indian System)
= Twenty-three lakh ten thousand one hundred four (In Indian numeration)
= 2,310,104 (In international numerals)
In simple words: Take numbers written in the International system and convert them to the Indian system by placing commas after the hundreds place, then every two digits. Then write down their new names in lakhs.

Exam Tip: Remember that 1 million is equal to 10 lakhs. So, 2 million is 20 lakhs, which helps you convert 2,310,104 into twenty-three lakh ten thousand one hundred four.