GSEB Class 6 Maths Solutions Chapter 2 પૂર્ણ સંખ્યાઓ Exercise 2.1

Question 1. Write the three natural numbers that come immediately after 10,999.
Answer: The three natural numbers that come right after 10,999 are:
\( 10,999 + 1 = 11,000 \)
\( 11,000 + 1 = 11,001 \)
\( 11,001 + 1 = 11,002 \)
So, the numbers are 11,000; 11,001; 11,002.
In simple words: To find the numbers right after another number, you just add one each time. We started with 10,999 and added one three times to get the next three natural numbers.

Exam Tip: Natural numbers start from 1. To find a successor, always add 1 to the given number.

Question 2. Write the three whole numbers that come immediately before 10,001.
Answer: The three whole numbers that come right before 10,001 are:
\( 10,001 - 1 = 10,000 \)
\( 10,000 - 1 = 9999 \)
\( 9999 - 1 = 9998 \)
So, the numbers are 10,000; 9999; 9998.
In simple words: To find the numbers that come just before another number, you simply subtract one each time. We started with 10,001 and took away one three times to find the preceding whole numbers.

Exam Tip: Whole numbers start from 0. To find a predecessor, always subtract 1 from the given number.

Question 3. Which is the smallest whole number?
Answer: The smallest whole number is 0 (zero).
In simple words: When we count whole numbers, we always start with the number zero. So, zero is the tiniest whole number we have.

Exam Tip: Remember that natural numbers start from 1, but whole numbers include 0, making 0 the smallest whole number.

Question 4. State the whole numbers that lie between 32 and 53.
Answer: The whole numbers that come between 32 and 53 are as follows:
33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51 and 52.
Therefore, there are a total of 20 whole numbers between 32 and 53.
A quick method to find the total count is: \( (53 - 32) - 1 = 21 - 1 = 20 \).
Note: When we talk about numbers *between* 32 and 53, we do not include 32 and 53 themselves.
In simple words: We need to list all the whole numbers that are bigger than 32 but smaller than 53. There are exactly 20 such numbers.

Exam Tip: When finding numbers *between* two given numbers, always subtract both the start and end numbers and then subtract 1 from the result to get the correct count.

Question 5. State the number that comes immediately after each of the following numbers:
(a) 24,40,701
(b) 1,00,199
(c) 10,99,999
(d) 23,45,670
Answer: To get the number that comes immediately after, we need to add 1 to the given number.
(a) The number immediately after 24,40,701 is \( 24,40,701 + 1 = 24,40,702 \).
(b) The number immediately after 1,00,199 is \( 1,00,199 + 1 = 1,00,200 \).
(c) The number immediately after 10,99,999 is \( 10,99,999 + 1 = 11,00,000 \).
(d) The number immediately after 23,45,670 is \( 23,45,670 + 1 = 23,45,671 \).
In simple words: For each number, we just add one to it to find the very next number in the counting sequence.

Exam Tip: Pay close attention to carrying over when adding 1, especially with numbers ending in 9s, to avoid common calculation errors.

Question 6. State the number that comes immediately before each of the following numbers:
(a) 94
(b) 10,000
(c) 2,08,090
(d) 76,54,321
Answer: To get the number that comes immediately before, we need to subtract 1 from the given number.
(a) The number immediately before 94 is \( 94 - 1 = 93 \).
(b) The number immediately before 10,000 is \( 10,000 - 1 = 9999 \).
(c) The number immediately before 2,08,090 is \( 2,08,090 - 1 = 2,08,089 \).
(d) The number immediately before 76,54,321 is \( 76,54,321 - 1 = 76,54,320 \).
In simple words: For each number, we just take away one from it to find the number that came right before it in the counting sequence.

Exam Tip: Be careful with borrowing when subtracting 1, especially from numbers like 10,000, to ensure accuracy.

Question 7. From the given pairs of numbers, state which number will appear on the left side on a number line and which will appear on the right side. Also, state which sign (<, >) will be used between them:
(a) 530, 503
(b) 370, 307
(c) 98,765; 56789
(d) 98,30,415; 1,00,23,001
Answer:
(a) 530, 503
On the number line, 503 is to the left of 530.
This is because 530 is a larger number than 503.
\( \implies 530 > 503 \)
(b) 370, 307
On the number line, 307 is to the left of 370.
This is because 370 is a larger number than 307.
\( \implies 370 > 307 \)
(c) 98,765; 56789
On the number line, 56,789 is to the left of 98,765.
This is because 98,765 is a larger number than 56,789.
\( \implies 98,765 > 56,789 \)
(d) 98,30,415; 1,00,23,001
On the number line, 98,30,415 is to the left of 1,00,23,001.
This is because 98,30,415 is a smaller number than 1,00,23,001.
\( \implies 98,30,415 < 1,00,23,001 \)
In simple words: On a number line, smaller numbers are always on the left, and bigger numbers are always on the right. If a number is bigger, we use the '>' sign; if it's smaller, we use the '<' sign.

Exam Tip: Always remember that the value of a number increases as you move from left to right on a number line. The 'greater than' (>) sign points to the smaller number, and the 'less than' (<) sign points to the smaller number.

Question 8. State whether each of the following statements is True (V) or False (X):
(a) Zero is the smallest natural number.
(b) 400 is the number that comes before 399.
(c) Zero is the smallest whole number.
(d) 600 is the number that comes after 599.
(e) Every natural number is a whole number.
(f) Every whole number is a natural number.
(g) The number that comes before a two-digit whole number cannot be a single-digit number.
(h) 1 is the smallest whole number.
(i) There is no number before natural number 1.
(j) A whole number has no number before it.
(k) Whole number 13 is between numbers 11 and 12.
(l) Whole number 0 has no number before it.
(m) The number that comes after a two-digit number is always a two-digit number.
Answer:
(a) False, because zero is not the smallest natural number. Zero is the smallest whole number.
(b) False, because the number immediately before 399 is \( 399 - 1 = 398 \), not 400.
(c) True, because whole numbers begin with 0.
(d) True, because the number immediately after 599 is \( 599 + 1 = 600 \).
(e) True, because all natural numbers (1, 2, 3...) are also part of the set of whole numbers (0, 1, 2, 3...).
(f) False, because every whole number is not a natural number. Zero is a whole number but not a natural number.
(g) False, because 10 is a two-digit whole number, and the number immediately before it is \( 10 - 1 = 9 \), which is a single-digit number.
(h) False, because 0 is the smallest whole number, not 1.
(i) True, because natural numbers start from 1, so there is no natural number smaller than 1.
(j) False, because whole number 1 has 0 as the number before it.
(k) False, because 13 is a larger number than both 11 and 12. A larger number cannot be *between* two smaller numbers.
(l) True, because whole numbers start from 0, so there is no whole number that comes before 0.
(m) False, because the number immediately after the two-digit number 99 is \( 99 + 1 = 100 \), which is a three-digit number.
In simple words: We're checking if each statement about numbers is correct or incorrect. We need to remember the definitions of natural and whole numbers and how they are ordered. Some statements are tricky and need us to think about edge cases, like what happens before 1 or after 99.

Exam Tip: Clearly understand the definitions of natural numbers (1, 2, 3...) and whole numbers (0, 1, 2, 3...). Always test statements with examples, especially those involving the smallest or largest numbers in a set, to verify if they are true or false.