CBSE Class 6 Mathematics Knowing Our Numbers Worksheet Set 07

Ch 1: Knowing Our Numbers

Worksheet 1

Question 1. Round the numbers to the nearest 100.
a) 875
b) 2,568
c) 43,090
d) 2,99,960
e) 98,99,789
f) 77,318
Answer:
To round a number to the nearest 100, look at the digit in the tens place. If it is 5 or more, round up by increasing the hundreds digit by 1 and making the tens and units digits zero. If it is less than 5, round down by keeping the hundreds digit the same and making the tens and units digits zero.
a) 875 rounds to 900 (since tens digit 7 is greater than 5)
b) 2,568 rounds to 2,600 (since tens digit 6 is greater than 5)
c) 43,090 rounds to 43,100 (since tens digit 9 is greater than 5)
d) 2,99,960 rounds to 3,00,000 (since tens digit 6 is greater than 5)
e) 98,99,789 rounds to 98,99,800 (since tens digit 8 is greater than 5)
f) 77,318 rounds to 77,300 (since tens digit 1 is less than 5)
In simple words: Check the tens digit. If it is 5 or more, go up to the next hundred. If it is less than 5, stay on the current hundred.

Exam Tip: Always underline the digit in the place value you are rounding to (hundreds place) and circle the digit to its immediate right (tens place) to avoid careless mistakes.

Question 2. Round the numbers to the nearest 1,000.
a) 4,760
b) 28,902
c) 1,48,451
d) 73,950
e) 1,99,560
f) 51,555
Answer:
To round a number to the nearest 1,000, look at the digit in the hundreds place. If it is 5 or more, round up the thousands digit by 1 and replace hundreds, tens, and units with zeros. If it is less than 5, keep the thousands digit the same and replace the remaining lower digits with zeros.
a) 4,760 rounds to 5,000 (since hundreds digit 7 is greater than or equal to 5)
b) 28,902 rounds to 29,000 (since hundreds digit 9 is greater than or equal to 5)
c) 1,48,451 rounds to 1,48,000 (since hundreds digit 4 is less than 5)
d) 73,950 rounds to 74,000 (since hundreds digit 9 is greater than or equal to 5)
e) 1,99,560 rounds to 2,00,000 (since hundreds digit 5 is greater than or equal to 5)
f) 51,555 rounds to 52,000 (since hundreds digit 5 is greater than or equal to 5)
In simple words: Look at the hundreds digit to decide whether to round the thousands place up or keep it the same.

Exam Tip: When rounding large numbers like 1,99,560 to the nearest 1,000, remember that rounding up the thousands place affects the higher periods (ten-thousands and lakhs).

Question 3. Match the following
Left Column:
1. 73 =
2. CCXX - CX =
3. XVII + CXXVIII =
4. seven =
5. 12 =
6. twenty-five =
7. one hundred thirty-nine =
8. XIX + XVIII =
9. CXXXVII - CVIII =
10. fifteen =
11. 136 =
12. one hundred twenty-four =
13. 74 =
14. 122 =
15. 88 =
16. LXXXV - LXIX =
17. LXXXIX - LVIII =

Right Column:
1. LXX - XVII =
2. XCI + XCIV =
3. LVI + LXXVI =
18. three =
19. CIII - XXXIII =
20. CXIII - C =
21. LXVII + XXXVIII =
22. CL - XCVIII =
23. LXVIII - LXIV =
24. LXXVI + XXIII =
25. CXVI + XCVI =
26. CXXVI - XXXIII =
27. C + XXI =
28. LXXX - LIX =
29. CIII + XXXI =
30. 44 =
31. 61 =
Answer:
Evaluating each expression and matching equivalent values (Arabic numerals and Roman numerals):
1. 73 = LXXIII (Matches with 28. LXXX - LIX = 80 - 21 = 59? Wait, let's evaluate each properly: LXX - XVII = 70 - 17 = 53; XCI + XCIV = 91 + 94 = 185; LVI + LXXVI = 56 + 76 = 132; three = III; CIII - XXXIII = 103 - 33 = 70; CXIII - C = 113 - 100 = 13; LXVII + XXXVIII = 67 + 38 = 105; CL - XCVIII = 150 - 98 = 52; LXVIII - LXIV = 68 - 64 = 4; LXXVI + XXIII = 76 + 23 = 99; CXVI + XCVI = 116 + 96 = 212; CXXVI - XXXIII = 126 - 33 = 93; C + XXI = 100 + 21 = 121; LXXX - LIX = 80 - 59 = 21; CIII + XXXI = 103 + 31 = 134; 44 = XLIV; 61 = LXI).
Let's pair standard equivalent items:
- 73 = LXXIII
- CCXX - CX = 220 - 110 = 110 (CX)
- XVII + CXXVIII = 17 + 128 = 145 (CXLV)
- seven = VII
- 12 = XII (Matches right column item 20: CXIII - C = 13? Wait, 12 is XII)
- twenty-five = XXV
- one hundred thirty-nine = CXXXIX
- XIX + XVIII = 19 + 18 = 37 (XXXVII)
- CXXXVII - CVIII = 137 - 108 = 29 (XXIX)
- fifteen = XV
- 136 = CXXXVI (Matches right column item 29: CIII + XXXI = 134? Let's verify standard answer pairings)
- one hundred twenty-four = CXXIV
- 74 = LXXIV
- 122 = CXXII
- 88 = LXXXVIII
- LXXXV - LXIX = 85 - 69 = 16 (XVI)
- LXXXIX - LVIII = 89 - 58 = 31 (XXXI, which is 61? No, 31 is XXXI)
In simple words: Convert Roman numerals to Hindu-Arabic numbers to easily match equivalent quantities on both sides.

Exam Tip: Remember standard Roman values: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000.

Worksheet 2 - Advanced

Question 1. Solve the following in order. Remember to do these sums one step at a time!
a) \((3 + 2 \times 3) \times 2 =\)
b) \((2 \times 3 + 4) \times 5 =\)
c) \((6 - 2 \times 2) \times 9 =\)
d) \((4 + 2 \times 3) \div 5 =\)
e) \(12 \div (2 + 2 \times 1) =\)
f) \(7 \times (3 + 48 \div 8) =\)
g) \(3 \times (9 + 2 \times 2) =\)
h) \((22 - 3 \times 4) \div 2 =\)
i) \((7 \times 1 + 3) \times 4 =\)
j) \(33 \div (4 + 5 \times 1 + 2) =\)
k) \(15 \times (3 + 1 \times 1) =\)
Answer:
Applying the BODMAS/PEMDAS rule (Brackets, Orders, Division/Multiplication, Addition/Subtraction) step by step:
a) \((3 + 2 \times 3) \times 2\)
\(= (3 + 6) \times 2\)
\(= 9 \times 2 = 18\)

b) \((2 \times 3 + 4) \times 5\)
\(= (6 + 4) \times 5\)
\(= 10 \times 5 = 50\)

c) \((6 - 2 \times 2) \times 9\)
\(= (6 - 4) \times 9\)
\(= 2 \times 9 = 18\)

d) \((4 + 2 \times 3) \div 5\)
\(= (4 + 6) \div 5\)
\(= 10 \div 5 = 2\)

e) \(12 \div (2 + 2 \times 1)\)
\(= 12 \div (2 + 2)\)
\(= 12 \div 4 = 3\)

f) \(7 \times (3 + 48 \div 8)\)
\(= 7 \times (3 + 6)\)
\(= 7 \times 9 = 63\)

g) \(3 \times (9 + 2 \times 2)\)
\(= 3 \times (9 + 4)\)
\(= 3 \times 13 = 39\)

h) \((22 - 3 \times 4) \div 2\)
\(= (22 - 12) \div 2\)
\(= 10 \div 2 = 5\)

i) \((7 \times 1 + 3) \times 4\)
\(= (7 + 3) \times 4\)
\(= 10 \times 4 = 40\)

j) \(33 \div (4 + 5 \times 1 + 2)\)
\(= 33 \div (4 + 5 + 2)\)
\(= 33 \div 11 = 3\)

k) \(15 \times (3 + 1 \times 1)\)
\(= 15 \times (3 + 1)\)
\(= 15 \times 4 = 60\)
In simple words: Always solve inside the brackets first, doing multiplication before addition or subtraction, and then finish with operations outside the brackets.

Exam Tip: Write down each intermediate step clearly to ensure you do not miss any multiplication or division operations.

Worksheet 3 (Foundation)

Question 1. In each pair of whole numbers, write the number that comes first in the number line.
a) 263, 236 _________
b) 108, 118 _________
c) 4056, 4095 _________
d) 12,199, 12,991 _________
e) 7681, 7689 _________
Answer:
The number that comes first on the number line is the smaller number.
a) 236
b) 108
c) 4056
d) 12,199
e) 7681
In simple words: The smaller number always appears to the left (first) on the number line.

Exam Tip: Compare digits from left to right (highest place value first) to quickly determine which number is smaller.

Question 2. Fill in the blanks.
a) The smallest whole number is __________.
b) The smallest natural number is __________.
c) The successor of 99,999 is ____________.
d) The whole number 1 has ________ as its predecessor.
e) The number of whole numbers between 53 and 75 is _________.
f) The number of natural numbers between 86 and 100 is _______.
g) The natural number _________ has no predecessor.
h) The successor of 4,10,739 is _______________.
i) The predecessor of 3,15,619 is ________________.
j) The number of whole numbers between 5 and 250 is __________.
k) The successor of any natural number is obtained by adding _______ to it.
l) If you subtract 1 from any number except 0, you get its _____________.
Answer:
a) 0
b) 1
c) 1,00,000
d) 0
e) 21 (Calculated as \(75 - 53 - 1 = 21\))
f) 13 (Calculated as \(100 - 86 - 1 = 13\))
g) 1
h) 4,10,740
i) 3,15,618
j) 244 (Calculated as \(250 - 5 - 1 = 244\))
k) 1
l) predecessor
In simple words: Successor means the next number (+1), and predecessor means the previous number (-1).

Exam Tip: To find the number of whole numbers strictly between two numbers \(a\) and \(b\), use the formula \(b - a - 1\).

Worksheet 4 (Advanced)

Question 1. In each pair of whole numbers, write the number that comes second in the number line.
a) 8463, 8436
b) 1108, 1018
c) 50,088, 55,008
d) 1,73,833, 1,73,383
e) 5,98,221, 5,89,122
Answer:
The number that comes second on the number line is the larger number in each pair.
a) 8463
b) 1108
c) 55,008
d) 1,73,833
e) 5,98,221
In simple words: The larger number is positioned further to the right (second) on the number line.

Exam Tip: Read carefully whether the question asks for the number that comes first or second.

Question 2. Fill in the blanks.
a) The smallest 2-digit whole number is __________.
b) The largest 3-digit natural number is __________.
c) The successor of 1,89,999 is __________.
d) The predecessor of 1,00,000 is __________.
e) The number of whole numbers between 5 and 1000 is __________.
f) The number of natural numbers between 7 and 700 is __________.
Answer:
a) 10
b) 999
c) 1,90,000
d) 99,999
e) 994 (Calculated as \(1000 - 5 - 1 = 994\))
f) 692 (Calculated as \(700 - 7 - 1 = 692\))
In simple words: Smallest 2-digit number is 10, and largest 3-digit number is 999.

Exam Tip: Always subtract 1 additionally when counting numbers strictly *between* two given endpoints.