Practice Questions
Large Numbers Around Us
Identify the number of zeroes in one billion when written as a numeral.
Name the two main systems of numeration for reading and writing large numbers that are discussed in the chapter.
A special calculator has only one button: +1000. Calculate how many times this button must be pressed to get the number 2,50,000 on the screen.
Solve for the nearest ten lakh for the number 8,67,54,321.
Compare the value of one crore with ten million using the symbols '>', '<', or '='.
Justify why a business owner planning for a festival that 8,450 people are expected to attend might order 8,500 units of a product instead of rounding down to 8,400.
Define the term 'one crore' by stating how many 'lakhs' it is equal to.
A factory produces 15,000 toy cars each day. Calculate the total number of toy cars produced in the month of March (31 days). Write the final answer in both Indian and American systems.
A library has 1,25,000 books. If each bookshelf can hold 250 books, calculate the total number of bookshelves required to store all the books.
Formulate a rule to determine the minimum and maximum possible number of digits in the sum of a 5-digit number and a 6-digit number.
Write the number 'fifty-two lakh, three thousand, four hundred one' in numerals, using the correct placement of commas as per the Indian system.
Recall the value of 'one million' and state its equivalent in the Indian number system.
Describe how to write the number 78,921,092 in words according to the International System of Numeration.
Write the following numbers in words according to the Indian place value system: (a) 9,05,00,730 (b) 12,00,45,006
Explain the primary difference in the pattern of placing commas between the Indian and the International system of numeration. Provide an example for each using the number 876543210.
Using a calculator with buttons +1, +10, +100, +1000, +10000, determine the minimum number of button clicks required to form the number 47,308. Also, write the expression for this process.
Summarize the rule for rounding a number to the nearest lakh. Use the number 23,65,400 as an example to explain the process.
Identify which is greater: Ten million or One crore. Explain your reasoning by converting both to numerals.
Given the number 54321098. (a) Place commas according to the Indian system and write its number name. (b) Place commas according to the International system and write its number name.
Analyze the expression 5,88,123 - 2,11,987. First, estimate the difference by rounding each number to the nearest lakh. Then, calculate the exact difference and compare it with your estimate.
A student uses digits 0-9 exactly once to form the 10-digit number 9876543210. They claim this is the largest possible 10-digit number that can be formed. Critique this claim. Then, formulate the largest possible 10-digit number that is a multiple of 10, using each digit from 0-9 exactly once. Justify your formulation.
Analyze the number 7,05,00,301 and write its name in the Indian place value system.
Calculate the product of 484 \times 25 using the multiplication shortcut where 25 = \frac{100}{4}.
The population of Town A was 4,50,670 in 2010 and increased to 5,35,890 in 2020. The population of Town B was 3,98,400 in 2010 and increased to 4,99,500 in 2020. Analyze the data to determine which town had a greater increase in population and by how much.
A person decides to save money for a world tour costing ₹ 12,00,000. They can save ₹ 7,500 per month. Calculate how many months it will take to save the required amount. Convert the total time into years and months. Examine if they can complete their savings in 12 years.
A state government plans to build a highway 250 km long. The cost of construction is ₹ 2,00,00,000 per kilometer. The government has a budget of ₹ 450 crores for this project. Analyze if the budget is sufficient. If not, calculate the additional amount required. Express the total cost and the deficit in crores.
Critique the statement: 'A number rounded to the nearest lakh will always be different from the number rounded to the nearest ten lakh.' Formulate a counterexample to disprove this statement.
Evaluate the American system and the Indian system of numeration. Propose one reason why the American system might be considered more consistent for a global audience.
A student claims, 'To multiply any number by 125, you can just add three zeroes to the number and then divide by 8.' Evaluate this claim and justify your conclusion with a mathematical proof.
Using a calculator with only +1000 and +10 buttons, formulate two different procedures to display the number 23,450. Justify which of your proposed procedures is more efficient.
Critique Roxie's reasoning for determining the number of digits in the product of two 2-digit numbers. Her reasoning was: 'Smallest product is (3 digits). The product must be less than (a 5-digit number), so the product is 3 or 4 digits.' Propose a more precise argument for the maximum possible product.
Propose a method to estimate the result of without performing the exact division. Justify why your proposed method yields a reasonable approximation.
Design a 'thought experiment' to help a friend comprehend the magnitude of 1 billion seconds. Your design must include a central question, necessary assumptions (e.g., days in a year), step-by-step calculations, and a final, relatable conclusion.
Evaluate the claim: 'The product of a 4-digit number and a 5-digit number can sometimes be an 8-digit number.' Justify your answer by formulating both a supporting example and a counterexample (i.e., a case where the product is not 8 digits).
Analyze the product of the smallest 4-digit number and the largest 2-digit number. Without calculating the exact value, determine the number of digits in the product and justify your answer.
Convert the following values from the American system to the Indian system by writing their equivalent value in lakhs or crores: (a) 5 million (b) 200 million (c) 1 billion
List the five 'nearest neighbours' (nearest thousand, ten thousand, lakh, ten lakh, crore) for the number 4,85,21,789.
Describe the place value of the digit '7' in the following numbers using both the Indian and International systems: (a) 7,12,34,567 (b) 1,72,34,567 (c) 1,27,34,567 (d) 1,23,74,567
Explain the concepts of 'rounding up' and 'rounding down'. For a school trip with 1,845 students, describe a situation where it is appropriate to round this number up, and another situation where it might be acceptable to round down. Justify your choices.
A company's profit is reported as 'two hundred million, five hundred thousand' dollars in the American system. An Indian company reports a profit of 'twenty crore, ten lakh' rupees. If 1 dollar = ₹80, compare their profits in rupees to determine which is larger.
A number is written as 'Five billion two hundred seven million ninety thousand four hundred five' in the American system. (a) Write this number in figures, using commas according to the American system. (b) Write the same number in figures, using commas according to the Indian system. (c) Write the number name according to the Indian system. (d) Demonstrate the expanded form of this number based on the Indian place value system.
The population of City A increased from 43,01,326 to 84,25,970 between two censuses. The population of City B increased from 24,33,835 to 44,67,797 in the same period. Evaluate which city had a more significant growth. Justify your answer by considering both absolute increase and relative (proportional) increase.
Propose the largest 8-digit number you can create where the digit in the ten lakhs place is double the digit in the tens place, and all other digits are 9.
Create a word problem involving a comparison of large numbers (in crores) and requiring both addition and subtraction for its solution. The problem should be set in the context of national budgets.
Propose a new number system called the 'Hexa-Indian System' for reading large numbers. This system should use a new period called a 'Shankh' after 'Crore'. A 'Shankh' is 100 Crores. The comma placement rule is 3-2-2-2, starting from the right. Formulate the rules for this system and use them to write the number 54321098765 in numerals with correct commas and in words according to your system.