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Chapter 1: Problem 31

Convert the numbers to expanded form. $$10,241$$

Short Answer

Expert verified
10,241 = 1 脳 10,000 + 0 脳 1,000 + 2 脳 100 + 4 脳 10 + 1 脳 1

Step by step solution

01

Identify place values

Break down the number 10,241 into its place values. Identify the value of each digit based on its position: 1 in the ten thousands place0 in the thousands place2 in the hundreds place4 in the tens place1 in the ones place
02

Write each digit as a product of its place value

Express each digit as a product of its digit and its place value:1 脳 10,0000 脳 1,0002 脳 1004 脳 101 脳 1
03

Combine the terms correctly

Combine these products to write the original number in its expanded form:10,241 = 1 脳 10,000 + 0 脳 1,000 + 2 脳 100 + 4 脳 10 + 1 脳 1

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Key Concepts

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

Place Value
When working with numbers, understanding place value is essential.
Each digit in a number has a unique position, and this position determines its value. For example, in the number 10,241, the place values from left to right are:
  • Ten thousands
  • Thousands
  • Hundreds
  • Tens
  • Ones
Identifying these place values helps us understand the weight of each digit.
The digit '1' in the ten thousands place means 1 脳 10,000, while the '1' in the ones place just means 1 脳 1.
Breaking numbers into place values is a fundamental skill in mathematics that helps in various operations.
Number Decomposition
Number decomposition is the process of breaking down a number into its component parts.
In the context of the number 10,241, decomposition involves expressing each digit as a product of the digit and its place value.
For instance, 10,241 can be decomposed as follows:
  • 1 脳 10,000
  • 0 脳 1,000
  • 2 脳 100
  • 4 脳 10
  • 1 脳 1
By decomposing a number, you can see how each digit contributes to the total value.
This approach simplifies complex arithmetic, making it easier to understand and work with large numbers.
Mathematical Notation
Mathematical notation is a way of writing mathematical concepts succinctly and precisely.
When we write a number in its expanded form, we use notation to show the value of each digit.
For example, the number 10,241 in expanded form is written as:
\[ 10,241 = 1 \times 10,000 + 0 \times 1,000 + 2 \times 100 + 4 \times 10 + 1 \times 1 \]This notation provides a clear and unambiguous representation of the number, explicitly showing the contribution of each digit.
Learning to read and write numbers using mathematical notation is crucial for accurately communicating and solving mathematical problems.
It also forms the foundation for more advanced topics in mathematics.

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