Problem 20 - Fundamentals of Mathematics

Question

For following problems, give the value of the indicated digit in the given number. 5 in 599.

Step-by-Step Solution

Answer

The value of 5 in 599 is 500.

Step 1: Identify the Place Value

The given number is 599. We need to identify the position of the digit '5'. From left to right, the digit '5' is the first digit in this number, which means it's in the hundreds place.

Step 2: Determine the Place Value's Worth

Now that we have identified that the '5' is in the hundreds place, we need to calculate its actual worth. In the decimal number system, each place value represents a power of ten. Since '5' is in the hundreds place, we calculate:\[5 \times 100 = 500\]

Step 3: Conclusion: State the Value of the Digit

The value of the digit '5' in the number 599 is 500.

Key Concepts

Decimal Number System

The decimal number system is the most commonly used number system, especially for daily counting and financial calculations. It is also known as the base-10 system.

• This system utilizes ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
• Each symbol within a number has a different place value based on its position.
• The value of each place in a number is determined by powers of ten, which means that as you move from right to left, each place value is ten times greater than the one to its right.

For instance, in the number 599:

• The 9 on the far right represents 9 ones or 9 \( (9 \times 10^0) \).
• The next 9 represents 90, being in the tens place \( (9 \times 10^1) \).
• The 5 represents 500, being in the hundreds place \( (5 \times 10^2) \).

Understanding the decimal system is crucial because it is applied in most of our calculations and understanding how numbers work.

Digit Identification

Digit identification is an essential skill when working with numbers, particularly in the context of determining the value of individual digits within a larger number.

• The first step is to clearly identify each digit's position in the number.
• In our example of 599, start from left to right: the digits are 5, 9, and 9.
• Each digit occupies a different position and thus has a different value. For instance, the first 9 is in the tens place, and the last 9 is in the ones place.

Correctly identifying the position of each digit allows us to further calculate its positional value, which leads to understanding the complete value of the entire number.

Positional Value

Positional value is key to understanding how much each digit in a number represents within the decimal number system. This involves multiplying the digit by its respective place value.

• The positional value depends entirely on the position the digit holds in the sequence of numbers.
• For example, in 599, the 5 holds the position of hundreds, making its positional value 500 \( (5 \times 100) \).
• The first 9 is in the tens place, giving it a positional value of 90 \( (9 \times 10) \).
• The last 9 is in the ones place, hence its value is simply 9 \( (9 \times 1) \).

By recognizing the positional value, you gain insights into how numbers are built and what each digit contributes to the overall value of the number. This fundamental concept is what allows us to perform various mathematical operations with accuracy and precision.