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Chapter 1: Problem 1

Give the place value of each digit in the following numbers. $$78$$

Short Answer

Expert verified
In 78, 7 is in the ten's place (70), and 8 is in the one's place (8).

Step by step solution

01

Identify the Tens Place

The number 78 is a two-digit number. The first digit, from left to right, is 7, which stands in the 'tens' place. This means the digit represents 70 (7 times 10).
02

Identify the Units Place

The second digit in the number 78 is 8. This digit is in the 'units' or 'ones' place, which means it represents 8 (8 times 1).
03

Compile the Place Values

Based on the identification of each digit: for the number 78, the place value of the digit 7 is 70, and the place value of the digit 8 is 8.

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Key Concepts

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

Understanding the Tens Place
The tens place is an important concept when dealing with numbers, especially those with two or more digits. When we look at a number, such as 78, the tens place is the second digit from the right. This corresponds to the digit 7 in our example. Since it is in the tens place, it reveals the quantity of tens in that number.

To find the value that the tens place represents, simply multiply the digit by 10. For instance, in the number 78, the 7 in the tens place means 7 groups of ten, resulting in 70.
  • Recognize the position: It's the second digit from the right in any two-digit number.
  • Calculate the value: Multiply the digit by 10 to get its true value.
Understanding this concept helps in breaking down and interpreting larger numbers efficiently.
Examining the Units Place
The units place, also known as the ones place, is the last digit in any number and holds unique value by itself. In the case of the number 78, the digit in the units place is 8. This digit indicates the number of single units in the whole number.

To calculate its place value, you don鈥檛 need to multiply it by any power of ten. Each digit here stands on its own, as in 8 people or 8 apples. Key points to remember include:
  • Special Position: Always the rightmost digit in the number.
  • Its Value: Reflects the exact number since it is multiplied by 1.
Mastering the concept of the units place helps in making accurate estimates and calculations.
Understanding Two-Digit Numbers
Two-digit numbers form the foundation of learning place values, as they consist of both tens and units places. Numbers such as 78 are perfect examples, where each digit represents a different place value.

In a two-digit number:
  • The first digit (from the left) indicates how many tens there are.
  • The second digit tells you how many single units there are.
This division into tens and units is fundamental in mathematics:
  • Simplifies Calculation: Breaking down numbers helps perform operations like addition and subtraction.
  • Foundation for Larger Numbers: This concept extends to more complex numbers, teaching us how to manage larger digits systematically.
By dissecting two-digit numbers, students can enhance their understanding of how numbers are built.

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Mentally give a one-digit estimate for each of the following quotients. That is, for each quotient, mentally estimate the answer using one of the digits \(1,2,3,4,5,6,7,8,\) or 9 $$921 \div 442$$

Rewrite each of the following using the associative property of addition. $$(4+5)+9$$
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