Problem 459 - Prealgebra

Question

Find the place value of the given digits. \(472,981\) (a) 8 (b) 4 (c) 1 (d) 7 (e) 2

Step-by-Step Solution

Answer

80, 400,000, 1, 70,000, 2,000

Step 1: Identify the digit's position - for 8

In the number 472,981, the digit 8 is in the 'tens' place. The place value of a digit is determined by its position in the number.

Step 2: Calculate place value for 8

Since 8 is in the 'tens' place, its place value is calculated by multiplying 8 by 10: \[ 8 \times 10 = 80 \]

Step 3: Identify the digit's position - for 4

In the number 472,981, the digit 4 is in the 'hundred-thousands' place.

Step 4: Calculate place value for 4

Since 4 is in the 'hundred-thousands' place, its place value is calculated by multiplying 4 by 100,000: \[ 4 \times 100,000 = 400,000 \]

Step 5: Identify the digit's position - for 1

In the number 472,981, the digit 1 is in the 'units' place.

Step 6: Calculate place value for 1

Since 1 is in the 'units' place, its place value is calculated by multiplying 1 by 1: \[ 1 \times 1 = 1 \]

Step 7: Identify the digit's position - for 7

In the number 472,981, the digit 7 is in the 'ten-thousands' place.

Step 8: Calculate place value for 7

Since 7 is in the 'ten-thousands' place, its place value is calculated by multiplying 7 by 10,000: \[ 7 \times 10,000 = 70,000 \]

Step 9: Identify the digit's position - for 2

In the number 472,981, the digit 2 is in the 'thousands' place.

Step 10: Calculate place value for 2

Since 2 is in the 'thousands' place, its place value is calculated by multiplying 2 by 1,000: \[ 2 \times 1,000 = 2,000 \]

Key Concepts

place value system

The place value system is a way to determine the value of each digit in a number based on its position. In our number system, also called the decimal system or base-10, each place represents a power of 10.
The further left a digit is in a number, the greater its value. Here are some key points:

• Each digit has a unique place value
• Place values increase by powers of 10 as you move from right to left
• Examples of place values: units (or ones), tens, hundreds, thousands, etc.

Understanding the place value system makes big numbers manageable and helps us perform arithmetic operations more effectively.

digit positions

Digit positions in a number are crucial for identifying their place values. Let’s clarify how this works in the number 472,981.
Each digit occupies a specific position:

• The rightmost digit (1) is in the 'units' place.
• The second digit from the right (8) is in the 'tens' place.
• The third digit from the right (9) is in the 'hundreds' place.
• The fourth digit from the right (2) is in the 'thousands' place.
• The fifth digit from the right (7) is in the 'ten-thousands' place.
• The sixth digit from the right (4) is in the 'hundred-thousands' place.

Remember, knowing the position of a digit enables us to compute its place value accurately.

multiplication in place value

To find the place value of a digit, we multiply it by the value of its position.
Let's see the number 472,981:

• For the digit 8 in the 'tens' place: \[ 8 \times 10 = 80 \]
• For the digit 4 in the 'hundred-thousands' place: \[ 4 \times 100,000 = 400,000 \]
• For the digit 1 in the 'units' place: \[ 1 \times 1 = 1 \]
• For the digit 7 in the 'ten-thousands' place: \[ 7 \times 10,000 = 70,000 \]
• For the digit 2 in the 'thousands' place: \[ 2 \times 1,000 = 2,000 \]

This method of multiplication in place value helps us understand the contribution of each digit to the whole number. It breaks down complex numbers into simpler, more manageable parts.