CBSE Class 6 Maths Chapter 1 Number System NCERT Solutions

In the number 428721, the digit '2' appears in two places. The first '2' is in the tens place, so its place value is $2\; \backslash times\; 10\; =\; 20$. The second '2' is in the ten thousands place, so its place value is $2\; \backslash times\; 10000\; =\; 20000$. The product of these place values is $20\; \backslash times\; 20000\; =\; 400000$.

Therefore, option (C) is the correct answer.

To find the number, we evaluate the expanded form:

$$3\; \backslash times\; 10000\; +\; 7\; \backslash times\; 1000\; +\; 9\; \backslash times\; 100\; +\; 0\; \backslash times\; 10\; +\; 4\; =\; 30000\; +\; 7000\; +\; 900\; +\; 0\; +\; 4$$

Adding these values together:

$$30000\; +\; 7000\; +\; 900\; +\; 0\; +\; 4\; =\; 37904$$

Therefore, option (C) is the correct answer.

The greatest 7-digit number is 99,99,999. When we add 1 to this number:

$$9999999\; +\; 1\; =\; 10000000$$

The number 10,000,000 is equal to 1 crore (1,00,00,000 in the Indian system).

Therefore, option (D) is the correct answer.

The number 9578 has digits in the thousands, hundreds, tens, and ones places. To write its expanded form, we multiply each digit by its corresponding place value:

$$9578\; =\; 9\; \backslash times\; 1000\; +\; 5\; \backslash times\; 100\; +\; 7\; \backslash times\; 10\; +\; 8\; \backslash times\; 1$$

Therefore, option (B) is the correct answer.

To round 85642 to the nearest thousand, we look at the digit in the hundreds place, which is 6. Since 6 is greater than or equal to 5, we round up the digit in the thousands place. The thousands digit is 5, so we round it up to 6. The digits to the right of the thousands place become zeros.

Therefore, 85642 rounded to the nearest thousand is 86000. Option (D) is correct.

To form the largest 4-digit number, we should use the largest available digits in the highest place values (thousands, hundreds, tens, ones). The given digits are 5, 9, 2, and 6. The largest digit is 9. We are allowed to use one digit twice. To maximize the number, we use the digit 9 twice for the thousands and hundreds places. Then, we use the next largest digits, 6 for the tens place and 5 for the ones place.

This gives us the number 9965.

Therefore, option (C) is the correct answer.

In the Indian System of Numeration, we group digits using commas starting from the right. The first comma comes after the third digit (hundreds place), and subsequent commas come after every two digits. The place values are Ones, Tens, Hundreds, Thousands, Ten Thousands, Lakhs, Ten Lakhs, Crores, Ten Crores, etc.

For the number 58695376:

• Starting from the right, the first three digits are 376.
• The next group of two digits is 95.
• The next group of two digits is 86.
• The remaining digit is 5.

So, the number is written as 5, 86, 95,376.

Therefore, option (C) is the correct answer.

One million is a term used in the International System of Numeration and is equal to 1,000,000.

In the Indian System of Numeration, the place values are arranged as: Ones, Tens, Hundreds, Thousands, Ten Thousands, Lakhs (1,00,000), Ten Lakhs (10,00,000), Crores (1,00,00,000), etc.

Comparing 1,000,000 with the Indian System:

$$1,000,000\; =\; 10\; \backslash times\; 100,000\; =\; 10\; \backslash text\{\; Lakhs\}$$

Therefore, one million is equal to 10 lakh.

Option (B) is the correct answer.

When rounding a number to the nearest thousands, we look at the hundreds digit. If the hundreds digit is 5 or greater, we round up the thousands digit. If it is less than 5, we keep the thousands digit as it is. The digits to the right of the thousands place become zeros.

We want the greatest number that rounds to 5000. This means the thousands digit must be 5, and the hundreds digit must be less than 5 (to avoid rounding up to 6000), or if the hundreds digit is 5, the number must be the largest possible value less than 5500.

Let's examine the options:

• (A) 5001: Rounds to 5000 (hundreds digit is 0).
• (B) 5559: Rounds to 6000 (hundreds digit is 5, so round up).
• (C) 5999: Rounds to 6000 (hundreds digit is 9, so round up).
• (D) 5499: Rounds to 5000 (hundreds digit is 4).

Comparing the numbers that round to 5000 (5001 and 5499), the greatest among them is 5499.

Therefore, option (D) is the correct answer.