What is the difference of the place values of 3 in the following numbers?
(i) 23,435
(ii) [tex]$3,54,371$[/tex]
(iii) 30,003
Answer (1)
Identify the place values of the digit 3 in each of the given numbers: 23,435, 354,371, and 30,003.
List all the place values: 3,000, 30, 300,000, 300, 30,000, and 3.
Determine the largest and smallest place values: 300,000 and 3.
Calculate the difference between the largest and smallest place values: 300 , 000 − 3 = 299 , 997
299997
Explanation
Understanding the Problem We are given three numbers: 23,435, 354,371, and 30,003. Our goal is to find the difference between the place values of the digit 3 in each of these numbers. This means we need to identify the place value of each 3 and then subtract the smallest from the largest.
Place Value in 23,435 In the number 23,435, the digit 3 appears in the thousands place and the tens place. So, the place values are 3,000 and 30.
Place Value in 354,371 In the number 354,371, the digit 3 appears in the hundred thousands place and the hundreds place. So, the place values are 300,000 and 300.
Place Value in 30,003 In the number 30,003, the digit 3 appears in the ten thousands place and the ones place. So, the place values are 30,000 and 3.
Identifying Largest and Smallest Place Values Now, let's list all the place values we found: 3,000, 30, 300,000, 300, 30,000, and 3. The largest place value is 300,000, and the smallest place value is 3.
Calculating the Difference To find the difference, we subtract the smallest place value from the largest place value: 300 , 000 − 3 = 299 , 997
Final Answer Therefore, the difference between the largest and smallest place values of the digit 3 in the given numbers is 299,997.
Examples
Understanding place values and their differences is crucial in many real-life scenarios, such as managing finances or understanding large datasets. For instance, imagine you are analyzing a company's sales figures. If one region reports sales of $354,371 and another reports $23,435, knowing the place values helps you quickly understand the scale of sales in each region. The '3' in $354,371 represents $300,000, while the '3' in $23,435 represents only $3,000. The difference highlights the significant disparity in sales performance, guiding strategic decisions.
