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Chapter 1: Problem 6

Name the place held by the \(7 .\) $$57,414$$

Short Answer

Expert verified
Answer: The place value of the digit 7 in the number 57,414 is the thousands place.

Step by step solution

01

Write down the number.

Write down the given number: 57,414.
02

Identify the place value of each digit.

For the given number 57,414, the place values are as follows, starting from the rightmost digit to the leftmost digit: 4 is in the ones (or units) place (1) 1 is in the tens place (10) 4 is in the hundreds place (100) 7 is in the thousands place (1,000) 5 is in the ten thousands place (10,000)
03

Determine the place value of the digit 7.

In the number 57,414, the digit 7 is in the thousands place (1,000). So, the place held by the 7 is the thousands place.

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Key Concepts

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

Digit Identification
Digit identification is the process of recognizing and understanding the value and position of a digit within a number. Each digit in a number contributes to its overall value based on its position, which we refer to as its "place value."
It鈥檚 important to learn how to identify each digit accurately as it lays the groundwork for understanding more complex mathematical concepts such as addition, subtraction, and multiplication of large numbers.
For instance, in the number \(57,414\), you need to be able to identify each digit separately:
  • 4 is in the Ones place
  • 1 is in the Tens place
  • 4 is in the Hundreds place
  • 7 is in the Thousands place
  • 5 is in the Ten Thousands place
Understanding digit identification helps us break down numbers and facilitates arithmetic operations, making them easier to manage and solve.
Thousands Place
The thousands place is a key component in understanding higher numbers in mathematics. It represents the digit that is fourth from the right in a multi-digit number and is associated with one thousand units.
In any given number, when you count from the rightmost digit (the ones place), the fourth position will always be the thousands place. For example, in \(57,414\), the digit occupying the thousands place is 7.
The role of the thousands place is significant because:
  • It helps show how many groups of one thousand are present in a number.
  • It aids in understanding the size of numbers through place value.
  • It is crucial in the process of writing numbers in words or numerals for clarity.
Recognizing the thousands place is essential when performing calculations that require regrouping or when dealing with monetary values and statistics.
Number Decomposition
Number decomposition, also known as number breakdown, is the process of expressing a number as the sum of its place values. This concept not only helps in understanding how each digit contributes to the total value of the number but also in carrying out arithmetic operations more efficiently.
To decompose the number \(57,414\), you break it down based on the place value of each digit:
  • 57,414 = 5 脳 10,000
  • + 7 脳 1,000
  • + 4 脳 100
  • + 1 脳 10
  • + 4 脳 1
Engaging in number decomposition allows students to:
  • Understand complex arithmetic by handling smaller parts.
  • Visualize and hence solve large sums or subtractions more logically.
  • Notice patterns and relationships in numbers, which is important for algebra.
Number decomposition is a vital skill for mathematically approaching real-life problems, from budgeting to engineering calculations.

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