Problem 9 - Prealgebra

Question

In the following exercises, find the place value of the given digits. 579,601 (a) 9\(\quad\) (b) 6\(\quad\) (c) 0\(\quad\) (d) 7\(\quad\) (e) 5\(\quad\)

Step-by-Step Solution

Answer

9: 900, 6: 60, 0: 0, 7: 70,000, 5: 500,000

Step 1 - Understand Place Value

Place value refers to the value of a digit based on its position within a number. Each position represents a different power of 10.

Step 2 - Identify Each Digit's Position

Label each digit of the number 579,601 according to its position: --- 1 (Thousands), 0 (Hundreds), 6 (Tens), 9 (Hundreds), 7 (Ten Thousands), 5 (Hundred Thousands)

Step 3 - Find Place Value of 9

The digit 9 is in the hundreds place. Thus, the place value of 9 is 900.

Step 4 - Find Place Value of 6

The digit 6 is in the tens place. Thus, the place value of 6 is 60.

Step 5 - Find Place Value of 0

The digit 0 is in the hundreds place (within the last three digits, so hundreds). Thus, the place value of 0 is 0.

Step 6 - Find Place Value of 7

The digit 7 is in the ten thousands place. Thus, the place value of 7 is 70,000.

Step 7 - Find Place Value of 5

The digit 5 is in the hundred thousands place. Thus, the place value of 5 is 500,000.

Key Concepts

digit positions

When looking at a number, each digit has a specific position. These positions are crucial because they determine the value of each digit.
For example, in the number 579,601, the '5' is in the hundred thousands place, while the '1' is in the ones place. Each position in a number corresponds to a power of 10, which we'll further explore. Recognizing and labeling these positions help in understanding the overall value of the number. It's like reading a map; each point has its significance.

powers of 10

Each digit's position represents a different power of 10. This is a base-10 number system, which means each place value is ten times the value of the place to its right.
For example:

• Ones (10⁰)
• Tens (10¹)
• Hundreds (10²)
• Thousands (10³)

and so on. In the number 579,601, the digit '6' is in the tens place, represented as 10¹, meaning its place value is 60. Understanding powers of 10 makes it easier to decode any number's place value.

value of digits

Now that we understand the positions and powers of 10, we can determine the value of each digit in a number. Let's break down the number 579,601:

• The '5' in the hundred thousands place means 5 x 10⁵ = 500,000.
• The '7' in the ten thousands place means 7 x 10⁴ = 70,000.
• The '9' in the hundreds place means 9 x 10² = 900.
• The '6' in the tens place means 6 x 10 = 60.
• The '0' in the hundreds place means 0 x 100 = 0.
• The '1' in the ones place means 1 x 1 = 1.

Combining these values gives the full number. By breaking it down in this way, it is easy to see how each digit contributes to the overall value of the number.