Write the expanded form in each of the following. (a) 61,986 (b) 42,086 (c) 20,880 (d) 1,34,395 (e) 3,57,906
The correct answer and explanation is:
Correct Answers:
(a) 61,986 = 60,000 + 1,000 + 900 + 80 + 6
(b) 42,086 = 40,000 + 2,000 + 0 + 80 + 6
(c) 20,880 = 20,000 + 0 + 800 + 80 + 0
(d) 1,34,395 = 1,00,000 + 30,000 + 4,000 + 300 + 90 + 5
(e) 3,57,906 = 3,00,000 + 50,000 + 7,000 + 900 + 0 + 6
Explanation (300 words):
Expanded form is a way of expressing a number by breaking it down into the value of each digit according to its place value. This method helps learners understand how numbers are built from units, tens, hundreds, thousands, and higher place values like lakhs.
To write a number in expanded form, each digit is multiplied by its positional value. For example, in the number 61,986, the digit 6 is in the ten-thousands place, so it represents 60,000. The next digit, 1, is in the thousands place and represents 1,000, and so on. This continues down to the ones place. Writing numbers this way helps clarify the role of each digit and supports better understanding of number magnitude.
In part (b), 42,086 contains a zero in the hundreds place. The expanded form still includes each digit’s position, but since the value is zero, it contributes nothing, though it helps maintain structure. In part (c), 20,880 includes a zero in the thousands and ones places. While these zeros do not change the value, their placement shows that no units or thousands are present.
Parts (d) and (e) involve numbers in the Indian place value system, which uses lakhs. Here, 1,34,395 and 3,57,906 are broken down accordingly, where 1,00,000 and 3,00,000 represent lakhs, followed by ten-thousands, thousands, and so on.
Understanding expanded form is important for early math learning, estimation, mental math, and recognizing the structure of large numbers. It builds a strong foundation for operations such as addition, subtraction, and understanding decimals and number systems.