Problem 460 - Prealgebra

Question

Find the place value of the given digits. \(12,403,295\) (a) 4 (b) 0 (c) 1 (d) 9 (e) 2

Step-by-Step Solution

Answer

4: hundred thousands; 0: ten thousands; 1: ten millions; 9: tens; 2: millions

Step 1 - Identify the place values

First, determine the place value system. From right to left, the place values for each digit in a large number are: units, tens, hundreds, thousands, ten thousands, hundred thousands, millions, ten millions, and so on.

Step 2 - Locate the digit and its place value

Locate the digit within the number and determine its place value by counting the digits from right to left.

Step 3 - Find the place value of 4

The digit 4 in the number 12,403,295 is in the hundred thousands place, because it is the sixth digit from the right.

Step 4 - Find the place value of 0

The digit 0 is in the ten thousands place, because it is the fifth digit from the right.

Step 5 - Find the place value of 1

The digit 1 is in the ten millions place, because it is the eighth digit from the right.

Step 6 - Find the place value of 9

The digit 9 is in the tens place, because it is the second digit from the right.

Step 7 - Find the place value of 2

The digit 2 is in the millions place, because it is the seventh digit from the right.

Key Concepts

Understanding Digit Place Value

Place value helps us understand the value of each digit in a number based on its position. The position of a digit within a number is crucial, as it determines whether the digit represents units, tens, hundreds, thousands, and so on. Let's consider the number given:

12,403,295.

To break it down:

• The rightmost digit represents the units place
• The second digit from the right represents the tens place
• The third digit from the right represents the hundreds place

As we move further left, the values increase: thousands, ten thousands, hundred thousands, etc. Understanding these positions helps us quickly identify the value of each digit.

Identifying Place Value

To identify the place value of a digit, count its position from right to left. Here’s a quick guide using our example number 12,403,295:

• The digit '4' is six places from the right, so it is in the hundred thousands place.
• The digit '0' is five places from the right, so it is in the ten thousands place.
• The digit '1' is eight places from the right, making it the ten millions place.

By following this method, we can easily identify and understand the value each digit holds based on its place in the number.

Working With Large Numbers

Large numbers can seem daunting at first. However, breaking them down using place value makes them much simpler. Let's revisit our number 12,403,295.

• The millions place in this number is '2,' which means 2 million.
• The digit '4' in the hundred thousands place gives us 400,000.
• The digit '1' in the ten millions place means 10 million.

So, 12,403,295 is essentially a combination of 10 million, 2 million, 400,000, and so on. Recognizing large numbers by their component parts helps make large numbers more manageable and easier to understand.