Problem 66 - Fundamentals of Mathematics

Question

(Section 1.2) What is the value of 5 in the number \(504,216 ?\)

Step-by-Step Solution

Answer

The value of 5 is 500,000.

Step 1: Understanding Number Place Value

To find the value of a specific digit in a number, we need to understand the place value system. In the number 504,216, each digit represents a value depending on its position.

Step 2: Identifying the Position of the Number 5

In the number 504,216, the digit '5' is the first digit from the left. This indicates that it is in the hundred-thousands place.

Step 3: Calculating the Value of 5

The place value system tells us that a digit in the hundred-thousands place should be multiplied by 100,000. Thus, the value of the digit '5' in this position is calculated as: \( 5 \times 100,000 = 500,000 \).

Key Concepts

Number Positions

Understanding number positions is essential when dissecting a large number. Each digit occupies a specific position, and its value is determined by its location within the number. For instance, in a number like 504,216, positions are usually identified from right to left:

• the rightmost digit is in the _units_ place,
• then tens,
• hundreds,
• thousands, and so on.

The farther left a digit is, the greater its place value. This is a foundational aspect of our base-10 (decimal) numbering system. By knowing these positions, we can easily determine each digit's contribution to the overall number.

Hundred-Thousands

The hundred-thousands place is a crucial position in our number layout. In a large number, like 504,216, identifying this spot is as simple as counting from the right to the left. In this number, the digit '5' is at the sixth position from the right, which means it is set in the hundred-thousands place.
Understanding that a digit in the hundred-thousands position determines how many complete sets of 100,000 are in a number is key. For example, the digit '5' in 504,216 does not merely stand alone; it indicates the presence of five hundred-thousands within the entire number.
Recognizing this position is vital for correctly interpreting and calculating large quantities.

Digit Values

The value of a digit in any given position is determined by multiplying the digit by the positional value of its place. This calculation gives the digit its full value in the context of the entire number.

• If we consider the number 504,216, the digit '5' is in the hundred-thousands place.
• This dictates that we multiply 5 by 100,000.

This results in a value of 500,000 for the digit '5'. Therefore, each digit has two important parts to its identity: the digit itself and its place value.
Both parts determine how much the digit contributes to the overall number size. Understanding digit values can demystify any complex number by breaking it down into understandable, smaller units.