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Chapter 1: Problem 54

Write each whole number in expanded form. $$99,032$$

Short Answer

Expert verified
99,032 = 90,000 + 9,000 + 30 + 2.

Step by step solution

01

Identify Place Values

To write the number 99,032 in expanded form, first identify the place value of each digit. In this number: 9 is in the ten-thousands place, another 9 is in the thousands place, 0 is in the hundreds place, 3 is in the tens place, and 2 is in the ones place.
02

Represent Each Place Value

Convert each digit into the value it represents based on its place. For 99,032: \(9 \times 10,000 = 90,000\), \(9 \times 1,000 = 9,000\), \(0 \times 100 = 0\), \(3 \times 10 = 30\), and \(2 \times 1 = 2\).
03

Combine Values in Expanded Form

Write the number as a sum of its place values: \(90,000 + 9,000 + 0 + 30 + 2\).

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Key Concepts

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

Place Value
The concept of place value is foundational in mathematics. It helps us understand the value of each digit in a number based on its position. Each position in a number has a different value, such as ones, tens, hundreds, and so on. For example, in the number 99,032, each digit is part of this system:
  • The first '9' represents tens of thousands.
  • The second '9' is in the thousands place.
  • The '0' is in the hundreds place, though its value is also zero.
  • The '3' is in the tens place.
  • The '2' is in the ones place.
Understanding place value is crucial for interpreting numbers and performing arithmetic operations effectively. It forms the basis for many learning objectives in early mathematics education.
Whole Numbers
Whole numbers are simple numbers that do not include any fractions or decimals. They start from zero and move upwards, such as 0, 1, 2, 3, etc. These numbers are used in the most basic counting and are crucial for understanding more complex mathematical concepts.
Important aspects of whole numbers include:
  • Being non-negative: Whole numbers are always zero or positive.
  • Being countable and having no decimal component.
  • Used in basic arithmetic operations like addition, subtraction, multiplication, and division.
By using whole numbers in exercises like converting them into expanded forms, students can better grasp their structure and composition, leading to a deeper understanding of how larger numbers work.
Mathematics Education
Mathematics education involves more than just numbers; it's about understanding concepts that build a foundation for problem-solving and logical thinking. During the early years, key topics such as place value and whole numbers are emphasized, forming the groundwork for later mathematical learning.
Effective mathematics education focuses on:
  • Developing numerical literacy, which includes recognizing and understanding different number forms.
  • Building skills in dealing with numbers efficiently, such as through operations or interpreting their values in various forms.
  • Encouraging reasoning skills, where students learn to approach and solve problems methodically.
With a solid educational framework, students develop confidence in using numbers, thus preparing them for more advanced mathematical challenges in the future.

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