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Chapter 1: Problem 32

Convert the numbers to expanded form. $$20,873$$

Short Answer

Expert verified
20,873 = 20,000 + 800 + 70 + 3

Step by step solution

01

Identify the place value of each digit

Break down the number into its individual digits and identify the place value for each digit in the number 20,873. The digits and their place values are: 2 (ten thousands), 0 (thousands), 8 (hundreds), 7 (tens), and 3 (units).
02

Multiply each digit by its place value

Represent each digit multiplied by its corresponding place value:- 2 in the ten thousands place: \( 2 \times 10,000 = 20,000 \)- 0 in the thousands place: \( 0 \times 1,000 = 0 \)- 8 in the hundreds place: \( 8 \times 100 = 800 \)- 7 in the tens place: \( 7 \times 10 = 70 \)- 3 in the units place: \( 3 \times 1 = 3 \)
03

Combine the expanded values

Add all the values obtained from step 2 to get the expanded form:\( 20,000 + 0 + 800 + 70 + 3 = 20,873 \)So, the number 20,873 can be written in expanded form as \( 20,000 + 800 + 70 + 3 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Place Value
Understanding place value is essential in expanding numbers. Each digit in a number has a specific value based on its position. In the number 20,873, the digit 2 is in the ten thousands place, giving it a value of 20,000. Similarly, the 0 is in the thousands place, giving it a value of 0. The digit 8 is in the hundreds place, so it has a value of 800. The digit 7 is in the tens place, making its value 70, and the digit 3 is in the units place, giving it a value of 3. Recognizing the place value of each digit helps in breaking down complex numbers and makes arithmetic operations easier.
Number Decomposition
Number decomposition involves breaking down a number into its fundamental parts based on place value. For example, the number 20,873 can be decomposed into its place values as follows:

  • 20,000 (ten thousands place)

  • 0 (thousands place)

  • 800 (hundreds place)

  • 70 (tens place)

  • 3 (units place)


This step-by-step decomposition allows us to understand the contribution of each digit to the overall number. It also simplifies the process of performing arithmetic operations, such as addition or subtraction.
Addition in Arithmetic
Addition is a fundamental arithmetic operation. It involves combining values to get a sum. When dealing with expanded forms, you add the values of each decomposed part to get the original number. For the number 20,873 decomposed into 20,000, 0, 800, 70, and 3, you add these values:

  • 20,000 + 0 = 20,000

  • 20,000 + 800 = 20,800

  • 20,800 + 70 = 20,870

  • 20,870 + 3 = 20,873


By adding the values in this sequence, you can verify the completeness of the expanded form. This technique is useful not only in understanding numbers but also in solving complex arithmetic problems efficiently.

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