Problem 55 - Fundamentals of Mathematics

Question

What is the value of 7 in \(44,763 ?\)

Step-by-Step Solution

Answer

The value of 7 in 44,763 is 700.

Step 1: Identify the Decimal System

In the decimal (base-10) system, each digit in a number has a specific place value. The place values are determined from right to left as: units (1), tens (10), hundreds (100), thousands (1,000), ten thousands (10,000), etc.

Step 2: Determine the Place Value of 7

In the number 44,763, the digit 7 is located in the hundreds place. To verify this, count the positions from right to left: 3 is in the units place, 6 in the tens place, and 7 in the hundreds place.

Step 3: Calculate the Value of 7

Since the 7 is in the hundreds place, its value is calculated as 7 times 100: \[ 7 \times 100 = 700 \]

Step 4: Conclude with the Identified Value

Therefore, the value of the digit 7 in the number 44,763 is 700.

Key Concepts

Decimal System

The decimal system, also known as the base-10 system, is the foundation of the number system we use in everyday life. It's called "decimal" because "deci-" signifies ten, and this system uses ten distinct symbols: 0 through 9. Each position in a decimal number has a different value based on powers of 10. This means that the value of a number increases by tenfold as you move left. For example:

• The first position to the rightmost side in a number represents units or ones (10⁰).
• The next position to the left signifies tens (10¹).
• This pattern continues with hundreds (10²), thousands (10³), and so on.

Understanding the decimal system is crucial because it allows you to interpret and calculate the value of numbers based on their positions. With this system, performing basic computational operations such as addition, subtraction, multiplication, and division becomes intuitive.

Hundreds Place

The hundreds place is a specific position in the decimal system and carries significant importance when determining the value of a digit within a number. It is the third position from the right in a multi-digit number. Let's look at the number 44,763 as an example:

• The digit 3 is in the units place (1).
• Moving left, 6 is in the tens place (10).
• The digit 7 is in the hundreds place (100).

For any digit in the hundreds place, its value is calculated by multiplying the digit by 100. In our example, since 7 is in the hundreds place, its contribution to the whole number is determined by computing: \[ 7 \times 100 = 700 \]. This means the 7 in 44,763 contributes 700 to the overall value of the number.

Number Positions

Each position within a number corresponds to a specific place value, and these positions are fundamental to understanding how large or small a number is. Knowing the proper place value gives context to each digit's actual worth within the number.

• Units (1) - The rightmost position and helps denote quantities one by one.
• Tens (10) - Next position to the left; adds groups of ten.
• Hundreds (100) - Adds larger groups, one hundred at a time.
• Thousands (1,000) - Groups even bigger numbers.

The number 44,763 uses these positions to give specific value to each of its digits. Observing number positions helps us assign proper weight to digits farthest from the point of reference and aids in operations like addition and subtraction by pairing similar positional values.