Problem 580 - Prealgebra

Question

Find the place value of the given digits in the number 549,362. (a) 9 (b) 6 (c) 2 (d) 5

Step-by-Step Solution

Answer

9: 9,000; 6: 60; 2: 2; 5: 500,000

Step 1 - Identify the digit's position

Determine the position of each digit in the number 549,362. The position of each digit from right to left is as follows: units, tens, hundreds, thousands, ten thousands, hundred thousands.

Step 2 - Determine place value for 9

The digit 9 is in the thousands place. Therefore, its place value is calculated as: \[9 \times 1,000 = 9,000\]

Step 3 - Determine place value for 6

The digit 6 is in the tens place. Therefore, its place value is calculated as: \[6 \times 10 = 60\]

Step 4 - Determine place value for 2

The digit 2 is in the units place. Therefore, its place value is calculated as: \[2 \times 1 = 2\]

Step 5 - Determine place value for 5

The digit 5 is in the hundred thousands place. Therefore, its place value is calculated as: \[5 \times 100,000 = 500,000\]

Key Concepts

digits

Digits are the building blocks of numbers. Each digit in a number holds a specific position and has a particular value depending on its place in the number. For example, in the number 549,362, the digits are 5, 4, 9, 3, 6, and 2. Understanding digits is crucial because their positions determine the entire value of the number. Learning to identify and interpret the value of each digit helps build a strong foundation for more complex mathematical concepts.

numerical position

The numerical position of a digit in a number tells us where the digit is located. Positions can be categorized into units, tens, hundreds, thousands, and so on. In the number 549,362, all digits have a specific position: 2 is in the units place, 6 is in the tens place, 3 is in the hundreds place, 9 is in the thousands place, 4 is in the ten thousands place, and 5 is in the hundred thousands place. Each position tells us how much a digit contributes to the overall value of the number.

multiplication

Multiplication is used to find the place value of a digit. By multiplying the digit by its numerical position's corresponding value, we can determine its place value. For instance, to find the place value of the digit 9 in 549,362, we multiply 9 by 1,000 (since it's in the thousands place), giving us 9,000. This concept helps us understand how each digit influences the total value of a number and shows the importance of each position through multiplication.