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Chapter 1: Problem 8

Give the place value of each digit in the following numbers. $$450$$

Short Answer

Expert verified
The place values are: 4 is 400, 5 is 50, and 0 is 0.

Step by step solution

01

Understanding Place Value

Place value is the value of a digit depending on its position in the number. Each position represents a power of 10 depending on its place, starting from the right.
02

Identifying the Hundreds Place

The first digit on the left in the number 450 is 4. Since it is in the hundreds place, it represents 4 hundred or \( 4 \times 100 = 400 \).
03

Identifying the Tens Place

The next digit is 5 and it is in the tens place. This means it represents 5 tens or \( 5 \times 10 = 50 \).
04

Identifying the Units Place

The last digit is 0 and it is in the units place. This means it represents 0 ones or \( 0 \times 1 = 0 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Hundreds Place
In the number 450, the hundreds place is occupied by the digit 4. The hundreds place is significant because it tells us how many sets of 100 are in a number. To understand the importance of the hundreds place, think about the role of the digit 4 in our example. The 4 in 450 actually means 4 hundreds. So when we calculate the place value, we multiply 4 by 100, giving us 400. Some key things to remember about the hundreds place:
  • The hundreds place is the third place from the right in any whole number.
  • It helps us quickly understand large numbers by breaking them down into simpler portions of hundreds.
Knowing how to identify the hundreds place sets the foundation for understanding numbers in the thousands, ten thousands, and beyond.
Tens Place
Following the hundreds place, we find the tens place, which is the second digit from the right. In the number 450, the digit 5 sits here.The tens place represents how many groups of ten are in a number. By multiplying the digit in the tens place by 10, we get its place value. For 450, the 5 stands for 5 groups of ten, or 50 when we do the math: \[ 5 \times 10 = 50 \]Important points about the tens place include:
  • The tens place is crucial for understanding smaller increments within large numbers.
  • It simplifies larger numbers by grouping a whole set of tens together.
By mastering the tens place, you can better grasp more complex math topics and problem-solving techniques.
Units Place
The units place, sometimes called the ones place, is where we find the very last digit of a whole number. In our example with 450, the digit in the units place is 0.This location tells us how many single units are present in the number. For practical understanding, multiply the units digit by 1, which keeps its value unchanged. In this case, we compute:\[ 0 \times 1 = 0 \]Consider these highlights of the units place:
  • The units place is essential for precision, as it provides us with the exact count of individual units.
  • It always remains the farthest digit to the right in any number, regardless of size.
Understanding the units place lays the groundwork for reading any number accurately, no matter how many other places it has.

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Most popular questions from this chapter

Give the place value of each digit in the following numbers. $$45$$

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Find each of the following products. (Multiply.) In case use the shortcut method. $$\begin{array}{r}45 \\\\\times \quad 7 \\\\\hline\end{array}$$

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