Find the sum and difference of the place values of the underlined digits in the given numbers. (a) 85,43,65,930 (b) 29,82,43,926 (c) 9,16,48,532 (d) 14,83,16,526
The Correct Answer and Explanation is:
Let’s go through each part of the question step-by-step:
(a) 85,43,65,930
- The underlined digits are 4 (ten thousand place) and 6 (thousand place).
Place Value of 4 = 4 × 10,000 = 40,000
Place Value of 6 = 6 × 1,000 = 6,000
Sum = 40,000 + 6,000 = 46,000
Difference = 40,000 – 6,000 = 34,000
(b) 29,82,43,926
- The underlined digits are 2 (ten million place) and 4 (thousand place).
Place Value of 2 = 2 × 10,000,000 = 20,000,000
Place Value of 4 = 4 × 1,000 = 4,000
Sum = 20,000,000 + 4,000 = 20,004,000
Difference = 20,000,000 – 4,000 = 19,996,000
(c) 9,16,48,532
- The underlined digits are 1 (hundred thousand place) and 8 (thousand place).
Place Value of 1 = 1 × 100,000 = 100,000
Place Value of 8 = 8 × 1,000 = 8,000
Sum = 100,000 + 8,000 = 108,000
Difference = 100,000 – 8,000 = 92,000
(d) 14,83,16,526
- The underlined digits are 8 (million place) and 1 (hundred thousand place).
Place Value of 8 = 8 × 1,000,000 = 8,000,000
Place Value of 1 = 1 × 100,000 = 100,000
Sum = 8,000,000 + 100,000 = 8,100,000
Difference = 8,000,000 – 100,000 = 7,900,000
Explanation:
To find the sum and difference of the place values of underlined digits, follow these steps:
- Identify the place of each underlined digit. The place can be tens, hundreds, thousands, millions, etc.
- Multiply each digit by the value of its place. For example, in 85,43,65,930, the place value of 4 is in the ten thousand place, so you multiply 4 by 10,000.
- Add the place values for the sum. This gives you the total value when you combine both digits.
- Subtract the place values for the difference. This gives you the difference between the two digits in terms of their place values.
This process can be applied to any number, and knowing place values is crucial for understanding the size and significance of each digit in a number.
