Knowing Our Numbers

Numbers help us count, compare and measure. In this chapter you will compare large numbers, first by counting digits and then by comparing digits from the left, arrange them in ascending and descending order, and form the greatest and smallest numbers from given digits. You will read and write large numbers using place value, and learn the Indian system of numeration with commas after the hundreds, thousands and lakhs places (such as 5,08,01,592) and the International system with commas after every three digits from the right (such as 50,801,592). You will see that 1 lakh = 100 thousand and 1 million = 10 lakh. The chapter then shows how large numbers are used with units of length, mass and capacity, such as 1 km = 1000 m and 1 kg = 1000 g. You will learn to estimate sums, differences and products by rounding numbers to the nearest tens, hundreds or thousands, use brackets to simplify expressions, and read and write Roman numerals using I, V, X, L, C, D and M.

Detailed Worksheet: Knowing Our Numbers Section A - Definitions (10 marks) 1. What is meant by the place value of a digit? Write the place value of 7 in 4,73,215. (2 marks) 2. How many thousands make one lakh, and how many lakhs make one crore? (2 marks) 3. Write the rules for placing commas in the Indian system and the International system of numeration. (2 marks) 4. What is estimation? Why do we estimate the result of a calculation? (2 marks) 5. Write the values of the Roman symbols I, V, X, L, C, D and M. State the rule for writing a smaller symbol to the left of a larger one. (2 marks) Section B - Calculations and Applications (15 marks) 6. Using the digits 3, 8, 0, 5 and 7 only once, write (i) the greatest 5-digit number (ii) the smallest 5-digit number (iii) the difference between them. (3 marks) 7. Insert commas and write the number names in both systems: (i) 87595762 (ii) 99985102. (3 marks) 8. Round off: (i) 7826 to the nearest hundred (ii) 64,489 to the nearest thousand (iii) 945 to the nearest ten. Estimate the sum 5290 + 17986 by rounding each number to the nearest thousand. (3 marks) 9. A box of medicine contains 2,00,000 tablets, each weighing 20 mg. Find the total weight of all the tablets in grams and in kilograms. (3 marks) 10. Write in Roman numerals: (i) 49 (ii) 94 (iii) 1999. Write in Hindu-Arabic numerals: (iv) LXXIV (v) XCIX (vi) CDXL. (3 marks) Section C - Diagrams (10 marks) 11. Draw a place value chart in the Indian system with periods Crores, Lakhs, Thousands and Ones. Enter the number 3,20,45,608 in it and write its number name and expanded form. (4 marks) 12. Draw a place value chart in the International system with periods Millions, Thousands and Ones. Enter 32,045,608 in it and write its number name. (3 marks) 13. Draw a number line from 2000 to 3000 marked at every 100. Mark 2350 and 2780 and use the number line to round each to the nearest hundred. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. The populations of four towns are: Town A 2,35,471, Town B 2,53,174, Town C 2,35,714 and Town D 1,99,999. (i) Arrange them in ascending order. (ii) Which town has the largest population? (iii) Find the difference between the populations of Town B and Town D. (iv) Round each population to the nearest thousand. (5 marks) 15. A student wrote 7 x (8 + 2) = 7 x 8 + 2 = 58. (i) Find the correct value. (ii) Explain the mistake. (iii) Expand 15 x 102 using brackets as 15 x (100 + 2) and simplify. (iv) Why do brackets help in mental calculation? (5 marks) 16. A school sells 1,250 tickets for a fair at Rs 65 each. (i) Estimate the total collection by rounding both numbers to the nearest hundred and nearest ten. (ii) Find the exact collection. (iii) By how much does the estimate differ from the exact value? (iv) Is the estimate reasonable? Explain. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Place commas correctly in every large number and show the rounding used in each estimate.