Samacheer Kalvi Class 6 Maths Solutions Term 1 Chapter 1 Numbers Exercise 1.1

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 1 Numbers Ex 1.1

Question 1. Fill in the blanks.
1. The smallest 7 digit number is ______
2. The largest 8 digit number is ______
3. The place value of 5 in 7005380 is ______
4. The expanded form of the number 76,70,905 is ______
Answer:
1. The smallest 7 digit number is \( 10,00,000 \). This number is one followed by six zeros.
2. The largest 8 digit number is \( 9,99,99,999 \). This number is made up of eight nines.
3. The place value of 5 in 7005380 is \( 5 \times 1000 = 5000 \). The digit 5 is in the thousands place.
4. The expanded form of the number 76,70,905 is \( 7 \times 10,00,000 + 6 \times 1,00,000 + 7 \times 10,000 + 0 \times 1,000 + 9 \times 100 + 0 \times 10 + 5 \times 1 \). Each digit is multiplied by its place value.
In simple words: We find the smallest number by putting 1 followed by zeros. We find the largest number by using all nines. Place value tells us how much a digit is worth. Expanded form breaks a number into the sum of its digits multiplied by their place values.

🎯 Exam Tip: Remember to consider the number of digits when finding the smallest or largest numbers. The expanded form helps to understand the contribution of each digit to the total value.

Question 2. Say True or False.
1. In the Indian System of Numeration, the number 67999037 is written as 6,79,99,037.
2. The successor of a one-digit number is always a one-digit number \( 9 + 1 = 10 \).
3. The predecessor of a 3-digit number is always a 3 or 4 digit number \( 100 - 1 = 99 \).
4. \( 88888 = 8 \times 10000 + 8 \times 100 + 8 \times 10 + 8 \times 1 \).
Answer:
1. True. In the Indian system, commas are placed after the first three digits from the right, then every two digits, so 67999037 becomes 6,79,99,037.
2. False. The successor of a one-digit number can be a two-digit number. For example, the successor of 9 is 10.
3. False. The predecessor of a 3-digit number can be a 2-digit number. For example, the predecessor of 100 is 99, which has two digits.
4. False. The correct expanded form of 88888 should include the thousands place: \( 8 \times 10000 + 8 \times 1000 + 8 \times 100 + 8 \times 10 + 8 \times 1 \). The given expression is missing the \( 8 \times 1000 \) term.
In simple words: The first statement is true because of Indian comma rules. The second is false as 9's successor is 10 (two digits). The third is false as 100's predecessor is 99 (two digits). The fourth is false because the expanded form was missing a part for the thousands place.

🎯 Exam Tip: Carefully apply the rules for Indian and International numbering systems. Remember that 'successor' means adding 1, and 'predecessor' means subtracting 1.

Question 4. How many ten thousands are there in the smallest 6 digit number?
Answer:
The smallest 6-digit number is \( 1,00,000 \). This is also known as one lakh.
To find how many ten thousands are in it, we divide:
\( \frac{1,00,000}{10,000} = 10 \)
So, there are 10 ten thousands in the smallest 6-digit number. This is like asking how many groups of ten thousand you can make from one hundred thousand.
In simple words: The smallest 6-digit number is 1,00,000. When you divide 1,00,000 by 10,000, you get 10. So there are 10 ten thousands in 1,00,000.

🎯 Exam Tip: To find how many times one number is contained in another, use division. Make sure to identify the smallest number with the specified number of digits correctly.

Question 5. Using the digits 5, 2, 0, 7, 3 forms the largest 5 digit number and the smallest 5 digit number.
Answer:
Given digits are: 5, 2, 0, 7, 3
To form the largest 5-digit number, arrange the digits in descending order:
\( 7, 5, 3, 2, 0 \)
So, the largest 5-digit number is \( 75,320 \).
To form the smallest 5-digit number, arrange the digits in ascending order. However, 0 cannot be the first digit of a multi-digit number, so we place the next smallest digit first, then 0, followed by the remaining digits in ascending order:
\( 2, 0, 3, 5, 7 \)
So, the smallest 5-digit number is \( 20,357 \). Zero is placed in the second position to keep it a five-digit number.
In simple words: For the biggest number, put the digits from largest to smallest. For the smallest number, put the digits from smallest to largest, but never start with zero.

🎯 Exam Tip: When forming the smallest number with a given set of digits that includes zero, always place the smallest non-zero digit first, then zero, followed by the rest in ascending order.

Question 6. Observe the commas and write down the place value of 7.
(i) 56,74,56,345
(ii) 567,456,345
Answer:
(i) In 56,74,56,345 (Indian System), the digit 7 is in the Ten Lakhs place. Its place value is \( 7 \times 10,00,000 = 70,00,000 \).
(ii) In 567,456,345 (International System), the digit 7 is in the Millions place. Its place value is \( 7 \times 1,000,000 = 7,000,000 \). The position of commas helps to identify if the number system is Indian or International.
In simple words: For (i), 7 is in the ten lakhs place in the Indian system. For (ii), 7 is in the millions place in the International system.

🎯 Exam Tip: Pay close attention to the comma placement. Indian system uses 3, then 2, 2 digits. International system uses 3, 3, 3 digits from the right. This tells you which numbering system is being used.

Question 7. Write the following numbers in the International System by using commas.
1. 347056
2. 7345671
3. 634567105
4. 1234567890
Answer:
In the International System, commas are placed after every three digits from the right, moving leftwards.
1. \( 347,056 \)
2. \( 7,345,671 \)
3. \( 634,567,105 \)
4. \( 1,234,567,890 \)
This grouping of three digits makes it easier to read very large numbers in many parts of the world.
In simple words: To write numbers in the International System, put a comma after every three digits, starting from the right side.

🎯 Exam Tip: Remember the fixed pattern of comma placement (every three digits) for the International System. This is different from the Indian System.

Question 8. Write the largest six-digit number and put commas in the Indian and the International Systems.
Answer:
The largest six-digit number is \( 9,99,999 \).
Indian System: \( 9,99,999 \) (Nine Lakh Ninety-Nine Thousand Nine Hundred Ninety-Nine)
International System: \( 999,999 \) (Nine Hundred Ninety-Nine Thousand Nine Hundred Ninety-Nine)
While the numeral is the same, the way we say and punctuate it changes depending on the system.
In simple words: The largest six-digit number is 999999. In the Indian system, it's 9,99,999. In the International system, it's 999,999.

🎯 Exam Tip: Always state the number itself first, then apply the specific comma rules for each system. Practise writing out the number names for both systems.

Question 9. Write the number names of the following numerals in the Indian System.
(i) 75 32 105
(ii) 9,75,63,453
Answer:
(i) \( 75,32,105 \) is written as Seventy-five lakh thirty-two thousand one hundred five.
(ii) \( 9,75,63,453 \) is written as Nine crore seventy-five lakh sixty-three thousand four hundred fifty-three.
Remember that in the Indian system, 'lakh' and 'crore' are used instead of 'million' and 'billion'.
In simple words: (i) 75,32,105 is 'Seventy-five lakh thirty-two thousand one hundred five'. (ii) 9,75,63,453 is 'Nine crore seventy-five lakh sixty-three thousand four hundred fifty-three'.

🎯 Exam Tip: For the Indian system, remember the place values: ones, tens, hundreds, thousands, ten thousands, lakhs, ten lakhs, crores, ten crores.

Question 10. Write the number of names in words using the International System.
1. 345,678
2. 8,343,710
3. 103,456,789
Answer:
1. \( 345,678 \) is written as Three hundred forty-five thousand six hundred seventy-eight.
2. \( 8,343,710 \) is written as Eight million three hundred forty-three thousand seven hundred ten.
3. \( 103,456,789 \) is written as One hundred three million four hundred fifty-six thousand seven hundred eighty-nine.
The International System uses terms like 'thousand', 'million', and 'billion' in groups of three digits.
In simple words: We write these numbers by saying the digits in groups of three and then adding 'thousand', 'million', or 'billion'.

🎯 Exam Tip: When writing number names in the International System, always read digits in groups of three (e.g., "three hundred forty-five" before "thousand").

Question 11. Write the number name in numerals.
1. Two crores thirty lakhs fifty-one thousand nine hundred eighty.
2. Sixty-six million three hundred forty-five thousand twenty-seven.
3. Seven hundred eighty-nine million, two hundred thirteen thousand four hundred fifty-six.
Answer:
1. Two crores thirty lakhs fifty-one thousand nine hundred eighty is written as \( 2,30,51,980 \).
2. Sixty-six million three hundred forty-five thousand twenty-seven is written as \( 66,345,027 \).
3. Seven hundred eighty-nine million, two hundred thirteen thousand four hundred fifty-six is written as \( 789,213,456 \).
It helps to visualize the place value chart to correctly convert written names to numbers.
In simple words: We change the words for numbers into the actual number form. For example, "two crores" means \( 2,00,00,000 \).

🎯 Exam Tip: Pay close attention to whether the question asks for Indian or International system, as this changes the numbers like 'crores' vs 'millions'.

Question 12. Tamil Nadu has about twenty-six thousand three hundred forty-five square kilometres of Forest land. Write the number mentioned in the statement in the Indian System.
Answer:
The number mentioned is "twenty-six thousand three hundred forty-five".
In numerals, this is \( 26,345 \).
In the Indian System, this number would be written as \( 26,345 \) since it is a small number and the first comma would only appear at the thousands place if it were a lakh or crore value. This number describes the land area of forests in Tamil Nadu.
In simple words: The number "twenty-six thousand three hundred forty-five" is written as 26,345 in the Indian system.

🎯 Exam Tip: Always check if the number is large enough to require more complex comma placements for either system, or if it's a smaller number that looks the same in both systems.

Question 13. The number of employees in the Indian Railways is about 10 lakh. Write this in the International System of numeration.
Answer:
10 lakh in the Indian System is written as \( 10,00,000 \).
In the International System, \( 10,00,000 \) is read as One Million.
Therefore, 10 lakh is equal to \( 1,000,000 \) in the International System. This means 10 lakh people are equivalent to 1 million people.
In simple words: 10 lakh in the Indian system is the same as 1 million in the International system.

🎯 Exam Tip: Remember key conversions between the Indian and International systems, such as 1 Lakh = 100,000 and 1 Million = 1,000,000. So 10 Lakh = 1 Million.

Objective Type Questions

Question 14. 1 billion is equal to
(a) 100 crore
(b) 100 million
(c) 100 lakh
(d) 10000 lakh
Answer: (a) 100 crore
In simple words: In the International system, 1 billion is a very large number. In the Indian system, the same amount is called 100 crore. This shows a key conversion between the Indian and International numbering systems.

🎯 Exam Tip: Learn the equivalences between Indian and International numbering systems, such as 1 crore = 10 million, and 1 billion = 100 crore.

Question 15. The successor of 10 million is
(a) 1000001
(b) 10000001
(c) 9999999
(d) 100001
Answer: (b) 10000001
In simple words: The successor of a number is the number that comes right after it. To find the successor, you just add 1 to the original number. So, adding 1 to 10 million (10,000,000) gives 10,000,001.

🎯 Exam Tip: A successor is simply the number immediately following another, obtained by adding 1. A predecessor is obtained by subtracting 1.

Question 16. The difference between successor and predecessor of 99999 is
(a) 90000
(b) 1
(c) 2
(d) 99001
Answer: (c) 2
In simple words: The successor of 99999 is \( 99999 + 1 = 100000 \). The predecessor of 99999 is \( 99999 - 1 = 99998 \). The difference between these two numbers is \( 100000 - 99998 = 2 \). The difference between a number's successor and predecessor will always be 2.

🎯 Exam Tip: Always remember that the successor is \( n+1 \) and the predecessor is \( n-1 \). Their difference will always be \( (n+1) - (n-1) = 2 \).

Question 17. The expanded form of the number 6,70,905 is
(a) \( 6 \times 10000 + 7 \times 1000 + 9 \times 100 + 5 \times 1 \)
(b) \( 6 \times 10000 + 7 \times 1000 + 0 \times 100 + 9 \times 100 + 0 \times 10 + 5 \times 1 \)
(c) \( 6 \times 1000000 + 7 \times 10000 + 0 \times 1000 + 9 \times 100 + 0 \times 10 + 5 \times 1 \)
(d) \( 6 \times 100000 + 7 \times 10000 + 0 \times 1000 + 9 \times 100 + 0 \times 10 + 5 \times 1 \)
Answer: (d) \( 6 \times 100000 + 7 \times 10000 + 0 \times 1000 + 9 \times 100 + 0 \times 10 + 5 \times 1 \)
In simple words: The expanded form shows each digit multiplied by its place value (like ones, tens, hundreds, thousands, etc.). For the number 6,70,905, the 6 is in the lakh place, the 7 in the ten thousands place, 0 in thousands, 9 in hundreds, 0 in tens, and 5 in ones. This breaks the number down into the sum of the values of its digits. Writing a number in its expanded form helps to understand the value of each digit based on its position.

🎯 Exam Tip: To find the correct expanded form, identify the place value of each digit (Lakhs, Ten Thousands, Thousands, Hundreds, Tens, Ones) and multiply the digit by its corresponding place value.