Problem 70 Write the number in expanded for... [FREE SOLUTION]

Chapter 1: Problem 70

Write the number in expanded form. $$328,476$$

Short Answer

Expert verified

The expanded form of 328,476 is \[300,000 + 20,000 + 8,000 + 400 + 70 + 6\].

Step by step solution

Identify the Place Value

First identify the place value of each digit. For the number 328,476, the breakdown is as follows: \n$3 \times 100,000$, \n$2 \times 10,000$, \n$8 \times 1,000$, \n$4 \times 100$, \n$7 \times 10$, \n$6 \times 1$.

Writing in Expanded Form

Now write the number in expanded form. This means writing the number as a sum of its place values identified in step one. The expanded form of the number 328,476 is: \[ (3 \times 100,000)+ (2 \times 10,000)+ (8 \times 1,000)+ (4 \times 100)+ (7 \times 10) + (6 \times 1) \].

Simplification of Expanded Form

The expanded form can be simplified to: \[300,000 + 20,000 + 8,000 + 400 + 70 + 6\]. In terms of writing, the expanded form is 'three hundred thousand, plus twenty thousand, plus eight thousand, plus four hundred, plus seventy, plus six'.

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Key Concepts

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

Place Value in Mathematics

Understanding place value is essential for breaking down numbers into their expanded forms. Each digit in a number has a specific place value, which tells us how much that digit worth depends on its position.
For instance, in the number 328,476:

The digit '3' is in the hundred thousands place, so it represents three hundred thousand or $3 \times 100,000$.
The digit '2' is in the ten thousands place, representing twenty thousand or $2 \times 10,000$.
Moving to the right, '8' is in the thousands place, equaling eight thousand or $8 \times 1,000$.
The '4' is in the hundreds place, meaning four hundred or $4 \times 100$.
'7' is in the tens place, so it鈥檚 seventy or $7 \times 10$.
Lastly, '6' is in the ones place, simply equals six or $6 \times 1$.

Recognizing the place value helps in understanding the full representation of numbers, making complex problems easier to solve.

Number Representation in Expanded Form

Representing numbers in expanded form involves expressing them as the sum of each digit multiplied by its place value. This representation clearly shows how each digit contributes to the total number.
For 328,476, the expanded form is written as:

$(3 \times 100,000) + (2 \times 10,000) + (8 \times 1,000) + (4 \times 100) + (7 \times 10) + (6 \times 1)$

By expanding a number, we break it down into more manageable parts, making it easier to work with and understand conceptually. The expanded form demonstrates the hierarchical structure of number values.

Understanding Arithmetic Operations in Expanded Form

Arithmetic operations become more intuitive when dealing with numbers in their expanded form. It allows us to see, step by step, how a large number is put together by its individual components.
For example, simplifying the expanded form of 328,476 results in:

Three hundred thousand $300,000$
Twenty thousand $20,000$
Eight thousand $8,000$
Four hundred $400$
Seventy $70$
Six $6$

These smaller sums add up to form the whole number.
In addition, expanded form can help make arithmetic operations, such as addition and subtraction, clearer. You can perform operations digit by digit, ensuring accuracy, and gain more insight into how numbers work through these simple arithmetic processes.

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91影视

Write the number in expanded form. $$328,476$$

Short Answer

Step by step solution

Identify the Place Value

Writing in Expanded Form

Simplification of Expanded Form

Key Concepts

Place Value in Mathematics

Number Representation in Expanded Form

Understanding Arithmetic Operations in Expanded Form

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