NCERT Solutions Class 6 Maths Chapter 1 Exercise 1.1: Knowing Our Numbers

Understanding Indian and International Place Value Systems

To master the first exercise, we must understand how we read large numbers. Historically, different regions developed different ways of grouping digits. In India, we use the Indian System of Numeration, which groups digits in terms of thousands, lakhs, and crores. Globally, the International System of Numeration is used, grouping numbers in thousands, millions, and billions.

Commas play a vital role in both systems by separating 'periods' so we can read numbers at a glance. In the Indian system, the first comma comes after three digits from the right (ones, tens, hundreds), and subsequent commas come after every two digits. In the International system, commas are placed after every three digits from the right, consistently.

Comparison of Indian and International Systems

Step-by-Step: Solving Conversion Problems (Filling the Blanks)

1. Step 1: Write both values in numerical standard form — Write down the numbers on both sides of the equals sign using standard numbers. For example, if comparing '1 Lakh' and 'Ten Thousand', write down '1,00,000' and '10,000'.
2. Step 2: Count and compare the number of zeros — Count the zeros. 1 Lakh (1,00,000) has 5 zeros. Ten Thousand (10,000) has 4 zeros.
3. Step 3: Divide the larger number by the smaller number — Divide 1,00,000 by 10,000. $1,00,000 \div 10,000 = 10$. This means 1 Lakh equals 10 ten thousand.

Exam Tip: Avoiding Comma Mistakes

Always start placing commas from the right side (the ones place) of the number, not the left!

• Indian style rule: 3, 2, 2, 2... (First comma after 3 digits, then after every 2 digits).
• International style rule: 3, 3, 3, 3... (Comma after every 3 digits consistently).

If you write the commas from left to right, your entire place value representation will be incorrect, and you will lose marks!

Practice Questions with Solutions

• Q: Fill in the blank: 1 million = _______ hundred thousand. A: Step 1: Write down 1 million in international numeral form: 1,000,000 (which has 6 zeros). Step 2: Write down one hundred thousand: 100,000 (which has 5 zeros). Step 3: Divide the values: $1,000,000 \div 100,000 = 10$. Final answer: 10
• Q: Place commas correctly and write the numerals: Seventy-three lakh seventy-five thousand three hundred seven. A: Step 1: Write the number periods down according to the Indian system: Lakhs, Thousands, Ones. Step 2: Place the values: 73 Lakhs, 75 Thousands, 307 Ones. Step 3: Combine them and insert commas: 73,75,307. Final answer: 73,75,307
• Q: Insert commas suitably and write the name according to Indian System of Numeration: 87595762. A: Step 1: Group the number from the right according to the Indian system rule (3, 2, 2). Step 2: Placing commas gives: 8,75,95,762. Step 3: Read the periods: 8 Crore, 75 Lakh, 95 Thousand, 762. Final answer: 8,75,95,762 (Eight crore seventy-five lakh ninety-five thousand seven hundred sixty-two)
• Q: Insert commas suitably and write the name according to International System of Numeration: 78921092. A: Step 1: Group the number from the right according to the International system rule (3, 3). Step 2: Placing commas gives: 78,921,092. Step 3: Read the periods: 78 Million, 921 Thousand, 92. Final answer: 78,921,092 (Seventy-eight million nine hundred twenty-one thousand ninety-two)

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