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Chapter 1: Problem 28

Place the correct symbol, \(<\) or \(>,\) between the two numbers. $$5600 \quad 56,000$$

Short Answer

Expert verified
The correct symbol to place between 5600 and 56,000 is '>' . So, it will be 5600 < 56,000.

Step by step solution

01

Compare Number of Digits

First, we need to count the number of digits in each number. The number 5600 has four digits and the number 56,000 has five digits.
02

Determine Which Number is Greater

Since 56,000 has more digits than 5600, it is the greater number. So, we will place the '>' symbol between them.

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Key Concepts

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

Number of Digits
When comparing numbers, one of the first things to consider is the number of digits in each number. This is because the more digits a number has, the larger it is. For instance, if we look at the numbers 5600 and 56,000, we count the digits in both numbers.

  • 5600 has four digits: 5, 6, 0, 0.
  • 56,000 has five digits: 5, 6, 0, 0, and an additional 0.
A larger number of digits generally indicates a larger number because each additional digit increases the number's value significantly. By recognizing the number of digits, we can quickly identify that 56,000 is larger than 5600.

This method is a simple and effective way to compare numbers without diving into the specific values of each digit.
Greater Than and Less Than Symbols
In mathematics, the symbols used to indicate when one number is larger or smaller than another are the greater than symbol (\(>\)) and the less than symbol (\(<\)). These symbols are essential tools for illustrating relationships between numbers.

When using these symbols, keep in mind:
  • The "greater than" symbol \(>\) is used to show that the number on the left is larger than the number on the right.
  • The "less than" symbol \(<\) indicates that the number on the left is smaller than the number on the right.
For example, to compare 5600 and 56,000, we see that since 56,000 has more digits, it is greater. Thus, we appropriately place the greater than symbol between them: \( 5600 < 56,000 \).

Mastery of these symbols helps convey mathematical ideas clearly and efficiently, an essential skill in problem-solving.
Place Value in Numbers
Another critical concept in comparing numbers is understanding the place values of the digits in each number. Place value indicates the value of each digit based on its position within the number.

Let's examine a number like 56,000:
  • The 5 is in the ten-thousands place, representing 50,000.
  • The 6 is in the thousands place, representing 6,000.
  • The following zeros indicate hundreds, tens, and units, each valued as zero.
Understanding place value helps in comprehending why each digit contributes enormously to the total value of a number. Take 5600, where:
  • The 5 is in the thousands place, valued at 5,000.
  • The 6 is in the hundreds place, valued at 600.
  • The zeros are in the tens and units places, each being 0.
By knowing place value, you gain a deeper understanding of number size, which aids in making accurate comparisons and decisions about greater than or less than values.

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Most popular questions from this chapter

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