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Chapter 1: Problem 25

Write each of the following numbers in expanded form. $$4,587$$

Short Answer

Expert verified
The expanded form of 4,587 is \(4\times1000 + 5\times100 + 8\times10 + 7\times1\).

Step by step solution

01

Identify the Place Values

First, we identify the place values of each digit in the number 4,587. In this number, the digit '4' is in the thousands place, '5' is in the hundreds place, '8' is in the tens place, and '7' is in the ones place.
02

Write the Expanded Form

Next, express each digit as a product of its face value and its place value, and then write the expression as a sum: \[ 4\times1000 + 5\times100 + 8\times10 + 7\times1 \]

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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 crucial for breaking down numbers into more digestible parts. In our number system, each digit has a unique place value depending on its position.
Whether you're looking at simple numbers or very large ones, each place signifies a different power of ten.
  • The rightmost digit is always in the ones place, valued at 100 or 1.
  • The next digit to the left is in the tens place, valued at 101 or 10.
  • Move left again, and you've found the hundreds place, worth 102 or 100.
  • This sequence continues, increasing by a power of ten as you move left.

Understanding how these positions work is essential for mastering expanded forms and other fundamental number operations.
Thousands Place
The thousands place holds immense value because it represents a large chunk of the number.
For example, in the number 4,587, the '4' is in the thousands place, meaning it represents 4,000.
Essentially, this value is calculated as follows:
  • Imagine our number as: 4 thousands.
  • Mathematically, this translates to: \( 4 \times 1,000 = 4,000 \).
This concept helps you break down bigger numbers, showing you just how much value sits in a single digit when it's placed in the thousands position.
Hundreds Place
In the hundreds place, a single digit represents the number of complete hundreds.
In our example of 4,587, the '5' is situated in this position.
  • This placement means it is worth 500 since it is: \( 5 \times 100 = 500 \).
  • Each increase in this place adds another hundred to the total, emphasizing how quickly numbers grow as you move leftwards.
Understanding the hundreds place is not just about memorizing values, but also recognizing their contribution to the overall sum of the number.
Tens Place
The tens place might seem small but it carries significant weight in understanding a number's composition.
In 4,587, '8' occupies the tens place.
  • This means: \( 8 \times 10 = 80 \).
  • Each ten adds systematically to the total number, helping us track the nuances in value a digit can contribute.
By mastering the tens place, and others like it, you can easily deconstruct and reconstruct numbers, reinforcing core mathematical skills.

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Most popular questions from this chapter

Rewrite each of the following using the commutative property of addition. $$5+9$$

Find a solution for each equation. $$n+8=13$$

Find a solution for each equation. $$5+n=7$$

The application problems that follow may involve more than merely division. Some may require addition, subtraction, or multiplication, whereas others may use a combination of two or more operations. Monthly Income \(A\) family has an annual income of \(\$ 42,300 .\) How much is their monthly income?

Add each of the following. (All problems involve carrying in at least one column. $$\begin{array}{r} 36 \\ 46 \\ \hline \end{array}$$
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