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Chapter 1: Problem 29

Convert the numbers to expanded form. $$5203$$

Short Answer

Expert verified
5000 + 200 + 3

Step by step solution

01

- Identify each digit and its place value

In the number 5203, the digits and their corresponding place values are as follows: \[5\] is in the thousands place, \[2\] is in the hundreds place, \[0\] is in the tens place, and \[3\] is in the ones place.
02

- Write the value of each digit

Determine the value of each digit based on its place value: \[5 \times 1000 = 5000\], \[2 \times 100 = 200\], \[0 \times 10 = 0\], and \[3 \times 1 = 3\].
03

- Combine the values into expanded form

Combine the values from each place to get the expanded form: \[5000 + 200 + 0 + 3\]. Since adding zero does not change the sum, it can often be omitted for simplicity: \[5000 + 200 + 3\].

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Key Concepts

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

Place Value
Place value is a fundamental concept in mathematics that helps you understand the value of each digit in a number based on its position. For instance, in the number 5203, the digit \(5\) represents 5000 because it is in the thousands place. The digit \(2\) stands for 200 as it is in the hundreds place. The digit \(0\) is in the tens place, and it signifies zero because it has no value in this position. The digit \(3\) is in the ones place and holds the value of 3.
Number Representation
Number representation is a way to express a number in various forms such as standard form, expanded form, and word form. Understanding different forms of number representation can make mathematical concepts more understandable. For example, the number 5203 can be written in standard form as it is, or in expanded form, which breaks the number into each digit's place value. This gives us:
  • \(5000\) (the value of the digit \(5\) in the thousands place)
  • \(200\) (the value of the digit \(2\) in the hundreds place)
  • \(0\) (the value of the digit \(0\) in the tens place)
  • \(3\) (the value of the digit \(3\) in the ones place)
Putting these together, you get the expanded form: \(5000 + 200 + 0 + 3\). Note that \(0\) can be omitted to simplify: \(5000 + 200 + 3\).
Mathematics
In mathematics, breaking numbers down into their expanded forms can help simplify complex calculations and is essential for understanding arithmetic operations. Expanded form illustrates how much each digit in a number contributes to its overall value. For example, breaking down 5203 into \(5000 + 200 + 3\) can make it easier to perform operations such as addition, subtraction, and even understanding multi-digit multiplication.
  • Helps with Addition: Makes adding large numbers more manageable by aligning the place values.
  • Subtraction: Simplifies the process by making the numbers clearer and showing the direct subtraction of individual place values.
  • Multiplication: Understanding place values aids in breaking down larger numbers into simpler parts to multiply.
Expanded form is a key tool in foundational mathematics and aids students in grasping more complicated mathematical concepts as they progress in their education.

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