Problem 12 - Prealgebra

Question

In the following exercises, find the place value of the given digits. 78,320,465 (a) 8\(\quad\) (b) 4\(\quad\) (c) 2\(\quad\) (d) 6\(\quad\) (e) 7\(\quad\)

Step-by-Step Solution

Answer

(a) 10,000,000 (b) 1,000 (c) 10,000 (d) 1 (e) 10,000,000

Step 1: Understanding Place Value

Each digit in a number has a place value depending on its position from right to left. The units place is the rightmost position, followed by tens, hundreds, thousands, ten thousands, and so on.

Step 2: Identifying the Place Value of 8

The given number is 78,320,465. The digit 8 is in the ten millions place. Therefore, its place value is 10,000,000.

Step 3: Identifying the Place Value of 4

In the same number, the digit 4 is in the thousands place. Therefore, its place value is 1,000.

Step 4: Identifying the Place Value of 2

The digit 2 is in the ten thousands place. Therefore, its place value is 10,000.

Step 5: Identifying the Place Value of 6

The digit 6 is in the units place. Therefore, its place value is 1.

Step 6: Identifying the Place Value of 7

The digit 7 is in the ten millions place. Therefore, its place value is 10,000,000.

Key Concepts

Digits

One of the foundational aspects of understanding numbers is recognizing that they are made up of individual parts called digits. Each digit in a number holds a specific value relative to its position in the number. For example, the number 78,320,465 contains the digits: 7, 8, 3, 2, 0, 4, 6, and 5.

Digits themselves are basic units of numbers that range from 0 to 9. When we combine these digits in a specific order, they form larger numbers. Each digit is essential because it dictates the entire value of the number depending on where it is placed.

Understanding digits is the first step in mastering concepts like place value, number positions, and even comprehending large numbers.