Exercise 1.1 - Q1
Textbook Exercise Problem
Fill in the blanks: (a) 1 lakh = _____ ten thousand. (b) 1 million = _____ hundred thousand. (c) 1 crore = _____ ten lakh. (d) 1 crore = _____ million.
Step-by-Step Verified Solution:
- Step 1: Write numerical value of 1 lakh = 1,00,000. Ten thousand = 10,000. Dividing: 1,00,000 / 10,000 = 10.
- Step 2: 1 million = 1,000,000. Hundred thousand = 100,000. Dividing: 1,000,000 / 100,000 = 10.
- Step 3: 1 crore = 1,00,00,000. Ten lakh = 10,00,000. Dividing: 1,00,00,000 / 10,00,000 = 10.
- Step 4: 1 crore = 10,000,000. 1 million = 1,000,000. Dividing: 10,000,000 / 1,000,000 = 10.
Final Answer: (a) 10, (b) 10, (c) 10, (d) 10
Key Concept / Exam Strategy: Each place value step in both Indian and International base-10 systems multiplies by exactly 10.
Exercise 1.2 - Q5
Textbook Exercise Problem
Find the difference between the greatest and the least 5-digit number that can be written using the digits 6, 2, 7, 4, 3 each only once.
Step-by-Step Verified Solution:
- Step 1: To form the greatest 5-digit number, arrange digits in descending order: 7, 6, 4, 3, 2 -> 76,432.
- Step 2: To form the least 5-digit number, arrange digits in ascending order: 2, 3, 4, 6, 7 -> 23,467.
- Step 3: Subtract least from greatest: 76,432 - 23,467.
- Step 4: Calculation: 76,432 - 23,467 = 52,965.
Final Answer: Difference = 52,965
Key Concept / Exam Strategy: Descending order maximizes higher place-value weights; ascending order minimizes them.
Generated Exercise #1
Foundation
Question: Write the numeral for: "Seventy-three lakh seventy-five thousand three hundred seven" with appropriate commas in the Indian system.
Core Concept Tested: Indian place value system commas placement
Mentor Hint: Commas are placed after 3 digits from right, then every 2 digits.
Step-by-Step Solution:
- Step 1: Identify period values: Crores = 0, Lakhs = 73, Thousands = 75, Units period = 307.
- Step 2: Combine: 73,75,307.
Verified Answer: 73,75,307
Generated Exercise #2
Intermediate
Question: Estimate the product 578 × 161 by rounding off each number to its greatest place (hundreds).
Core Concept Tested: Estimation and general rounding off rules
Mentor Hint: 578 is closer to 600; 161 is closer to 200.
Step-by-Step Solution:
- Step 1: Round 578 to nearest hundred -> 600 (since tens digit 7 ≥ 5).
- Step 2: Round 161 to nearest hundred -> 200 (since tens digit 6 ≥ 5).
- Step 3: Multiply rounded values: 600 × 200 = 120,000.
Verified Answer: Estimated Product = 120,000
Generated Exercise #3
Intermediate
Question: Write the Roman numeral for 98 and 449.
Core Concept Tested: Roman numeral additive and subtractive rules
Mentor Hint: 90 = XC, 8 = VIII; 400 = CD, 40 = XL, 9 = IX.
Step-by-Step Solution:
- Step 1: For 98: 90 + 8 = (100 - 10) + 8 = XC + VIII = XCVIII.
- Step 2: For 449: 400 + 40 + 9 = (500 - 100) + (50 - 10) + (10 - 1) = CD + XL + IX = CDXLIX.
Verified Answer: 98 = XCVIII, 449 = CDXLIX
Generated Exercise #4
JEE-NEET Foundation
Question: A machine, on an average, manufactures 2,825 screws a day. How many screws did it produce in the month of January 2024?
Core Concept Tested: Calendar days application and multi-digit arithmetic
Mentor Hint: January always has 31 days regardless of leap year.
Step-by-Step Solution:
- Step 1: Number of days in January = 31 days.
- Step 2: Screws per day = 2,825.
- Step 3: Total production = 2,825 × 31 = 2,825 × (30 + 1) = 84,750 + 2,825 = 87,575 screws.
Verified Answer: 87,575 screws
Generated Exercise #5
Advanced HOTS
Question: Find the difference between the place value and face value of the digit 7 in the number 52,74,931.
Core Concept Tested: Place value vs face value distinction in large numbers
Mentor Hint: Face value is the digit itself (7); Place value is digit multiplied by its position weight (10,000).
Step-by-Step Solution:
- Step 1: Digit 7 is in ten-thousands place -> Place value = 7 × 10,000 = 70,000.
- Step 2: Face value of 7 = 7.
- Step 3: Difference = 70,000 - 7 = 69,993.
Verified Answer: 69,993