Problem 23 - Fundamentals of Mathematics

Question

For following problems, give the value of the indicated digit in the given number. 6 in 52,561,001,100.

Step-by-Step Solution

Answer

The value of the digit 6 is 600,000,000.

Step 1: Determine the Place Value

First, identify the place value of the digit 6 in the given number. The number is 52,561,001,100, and it reads as 52 billion, 561 million, 1 hundred, 100. The digit 6 is in the hundreds of million places.

Step 2: Express the Place Value in Numbers

Now, express the place value of 6 in numbers. Since 6 is in the hundreds of million places, it means it is worth 600,000,000.

Step 3: Combine the Place Value and Digit

Combine the digit with its place value to find the value of the 6 in the number. Thus, the digit 6 in the hundreds of million places stands for 600,000,000.

Key Concepts

Digit Value

Understanding the digit value is one of the fundamental steps in grasping place value concepts. The digit value is determined by multiplying a digit by its place value. This means the same digit can have different values depending on its position in a number. For example, the digit \(6\) can represent \(6\) units, \(60\) tens, or even \(600,000,000\) if it is located in the hundreds of million place, like in the number 52,561,001,100.
This approach allows us to express large numbers more efficiently and comprehend their size just by knowing each digit's contribution.
Working out the digit value involves:

• Identifying the digit's position within the number.
• Knowing the mathematical value of that position (like units, tens, hundreds, thousands, etc.).
• Calculating the digit times its place to understand its true worth in the larger number.

Number Reading

Reading large numbers can initially seem daunting, but it becomes straightforward once familiar with the place values each digit embodies. Each group of three digits is typically separated by a comma, marking thousands, millions, billions, and so on. This structured form allows you to systematically read the number from left to right.

For example, in the number 52,561,001,100, you'll read it as:

• "Fifty-two billion" for the first set, "52," located leftmost.
• "Five hundred sixty-one million" for the middle set, "561."
• "One thousand one hundred" for the final grouping, "001,100."

Breaking down the number into these segments helps to easily grasp even the largest numbers, following the pattern laid out by commas and place values.

Hundreds of Million Place

The hundreds of million place is crucial in understanding large values associated with billions and beyond. It's the third digit from the left in the millions period of a number.
In numbers like 52,561,001,100, the hundreds of million place holds significant weight. Here, the digit \(6\) is at this position, meaning it contributes \(600,000,000\) to the overall number.
This understanding is pivotal when managing large data figures, economics, and other fields where numerical representation of size is key. Each place has a multiplier:

• One hundred for the hundreds.
• One thousand when moved to the left to the thousands place.
• And increasingly from there, affecting millions, billions, and so forth.

Knowing the specific contribution of digits like the \(6\) in hundreds of millions place helps accurately depict and manipulate these large figures.