Problem 43 - Fundamentals of Mathematics

Question

What is the value of 5 in \(26,518,206 ?\)

Step-by-Step Solution

Answer

The value of 5 in 26,518,206 is 5,000.

Step 1: Identify the Place Value

When asking for the value of a digit in a number, first identify the place value of the digit. In the number \(26,518,206\), the digit 5 is in the thousands place. This means it represents five thousand (5000).

Step 2: Calculate the Numeric Value

Use the place value to calculate the numeric value that the digit represents. Since the digit 5 is in the thousands place, calculate: \[5 \times 1,000 = 5,000\]The value of the digit 5 in the number is therefore 5,000.

Key Concepts

Thousands Place

Place value is an important concept in understanding numbers. It tells us how much each digit in a number is worth depending on its position.
When we talk about the "thousands place," we are referring to the specific position in a number where the digit determines how many thousands are present. In any given number, the places are typically organized like this:

• Units
• Tens
• Hundreds
• Thousands
• Ten Thousands
• Hundred Thousands
• Millions, and so on.

In the number 26,518,206, the digit 5 is situated in the fourth position from the right, which is the thousands place. This means the 5 tells us there are five thousand units in that number. It’s as if you have five bundles, with each bundle containing a thousand items.

Numeric Value

The numeric value of a digit refers to the specific value it represents in its given place within the number.
This is determined by multiplying the digit by the value of its place. For example, a digit in the thousands place means it should be multiplied by 1,000.
If we take the number 26,518,206, we find the digit 5 in the thousands place. We calculate its numeric value by multiplying the digit 5 by 1,000: \[5 \times 1,000 = 5,000\]So, the numeric value of 5 in the number is 5,000. This multiplication shows us that the digit contributes five thousand to the overall value of the number.

Value of a Digit

Understanding the value of a digit is crucial when working with large numbers.
Every digit contributes to the total value of the number based on its position. This means each unique place changes the digit's value.
For instance, in the number 26,518,206, the digit 5, located in the thousands place, signifies five thousand. It contributes significantly to the entire number due to its high position.

• The value of a digit in the thousands place is found by multiplying the digit by 1,000
• It highlights how placement affects contribution: the same digit may have different values in different positions

In simpler terms, even though the digit is 5, its place in thousands makes it worth five thousand, vastly different from if it were in a lower place like units or tens.