Write the following numbers in the expanded form: (a) 75 432 (b) 37 911 (c) 10 956
The correct answer and explanation is:
Here is the expanded form of the given numbers:
(a) 75 432 = 70 000 + 5 000 + 400 + 30 + 2
(b) 37 911 = 30 000 + 7 000 + 900 + 10 + 1
(c) 10 956 = 10 000 + 900 + 50 + 6
Explanation (300 words):
Expanded form is a way of breaking down a number to show the value of each digit according to its place value. Every digit in a number has a specific value depending on its position from right to left. These positions are ones, tens, hundreds, thousands, ten thousands, hundred thousands, and so on.
In part (a), the number 75 432 consists of five digits. The digit 7 is in the ten thousands place, which gives it a value of 70 000. The 5 is in the thousands place and equals 5 000. The 4 stands for 400, 3 stands for 30, and 2 stands for 2. When written in expanded form, all these values are added to represent the full number.
In part (b), the number 37 911 has the digit 3 in the ten thousands place, which means 30 000. The 7 is in the thousands place, giving 7 000. The 9 is in the hundreds place for 900, the next digit 1 stands for 10, and the last 1 stands for 1.
In part (c), the number 10 956 has the digit 1 in the ten thousands place, which is 10 000. The digit 0 is in the thousands place, but it does not contribute value in expanded form and is skipped. The 9 stands for 900, the 5 for 50, and the 6 for 6.
Understanding expanded form helps in grasping the concept of place value and improves mental math skills, especially when performing operations like addition, subtraction, and estimation. It is a foundational concept in number sense and arithmetic.