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Chapter 4: Problem 19

In Exercises 9-22, write each Hindu-Arabic numeral in expanded form. 34,569

Short Answer

Expert verified
The expanded form of the Hindu-Arabic numeral 34,569 is: \[30000 + 4000 + 500 + 60 + 9\]

Step by step solution

01

Identify Each Place Value

The numeral 34,569 in Hindu-Arabic is a five-digit number. From right to left: the first place value is the units (ones), second is tens, third is hundreds, fourth is thousands, and fifth is ten thousands. So we have: 9 in the units place, 6 in the tens place, 5 in the hundreds place, 4 in the thousands place, and 3 in the ten thousands place.
02

Expand Each Digit

After identifying the place value for each digit, we multiply the digit by the place value. So we get the following: 9*1, 6*10, 5*100, 4*1000, and 3*10000
03

Write The Number In Expanded Form

Finally, we combine the results from step 2 and express the number in the expanded form by adding all expanded digits, which gives: 30000 + 4000 + 500 + 60 + 9

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Key Concepts

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

Hindu-Arabic numerals
The Hindu-Arabic numeral system is the most common numerical system used worldwide today. It's named after its origins, developed by Indian mathematicians and later adopted by the Arabs. This system includes 10 digits: 0 through 9.

The charm of this numeral system lies in its efficiency and simplicity. By using just these 10 digits, we can express any number imaginable.
  • It uses a base-10, or decimal system, meaning each place value corresponds to powers of 10.
  • The position of each digit in a number determines its value because of its place value system.
  • The inclusion of zero is essential as it allows for the expression of large values and empty place values.
This efficiency of representation empowers us to perform complex calculations and express any quantity, from the infinitesimally small to the incomprehensibly large.
Expanded form
The expanded form of a number offers a detailed look into the value of each digit, based on its position in the number. It is a way of writing numbers by showing the value of each digit.

Writing numbers in expanded form emphasizes the importance of place value. It breaks down a number into the sum of its parts, where each part is a product of the digit and its place value:
  • Example: The number 34,569 in expanded form is 30,000 + 4,000 + 500 + 60 + 9.
  • This form helps in understanding how each digit contributes to the entire number.
  • It reinforces the concept that each digit is not just a single unit, but a multiple of a power of 10 based on its position.
Understanding expanded form can aid in better grasping arithmetic operations and algebraic expressions, making it a foundational skill in mathematics.
Mathematical notation
Mathematical notation refers to symbols and notational conventions used to represent mathematical ideas and concepts. It provides a universal language for mathematics that transcends spoken languages.

In the context of place values and expanded form:
  • Digits are multiplied by powers of ten, represented by exponentiation, e.g., 101 for tens, 102 for hundreds.
  • Each part of the expanded form is written as a simple multiplication equation, such as 5 * 100 (or 5 脳 102).
Mathematical notation serves as a concise way to express complex mathematical ideas. By standardizing these representations, we ensure clear communication of mathematical procedures and concepts. It's like a shorthand that mathematicians all over the world understand, making collaboration and learning easier across the globe.

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Most popular questions from this chapter

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