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Chapter 5: Problem 50

Insert \(<,>,\) or \(=\) between each pair of numbers to form a true statement. $$ -0.59 \quad-0.52 $$

Short Answer

Expert verified
-0.59 < -0.52

Step by step solution

01

Understand the Concept

In this exercise, you need to compare two decimal numbers and insert the correct symbol (either `<`, `>`, or `=`) to make the statement true. A number is greater if it is further to the right on the number line.
02

Compare the Numbers

First, identify the numbers to compare: -0.59 and -0.52. Since both numbers are negative, the number closer to zero (less negative) is the larger number.
03

Analyze the Numbers

-0.59 is further from zero compared to -0.52, meaning -0.59 is more negative. Therefore, -0.59 is less than -0.52.
04

Insert the Correct Symbol

Since -0.59 is less than -0.52, we insert `<` between them. The statement now reads: -0.59 < -0.52.

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Key Concepts

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

Negative Numbers
Negative numbers are interesting and can sometimes be a little confusing. Let's break them down. A negative number is one that is less than zero. These numbers are found to the left of zero on a number line. When comparing negative numbers, it's essential to remember that the number which appears to be lesser (more negative) is actually smaller.
So, for two negative numbers like -0.59 and -0.52:
  • -0.59 is further from zero than -0.52.
  • This makes -0.59 more negative, hence, lesser than -0.52.
Always keep in mind that the closer a negative number is to zero, the larger it is.
Number Line Understanding
A number line is a visual representation of numbers placed at equal intervals along a line. Understanding a number line is crucial for comparing numbers.
When you think about a number line:
  • Positive numbers are to the right of zero, getting larger as you move right.
  • Negative numbers are to the left of zero, getting smaller as you move left.
  • This means the larger numbers, including negative numbers closer to zero, are on the right side of their more negative counterparts.
This understanding makes it clear why on a number line, -0.52 is larger than -0.59 because -0.52 is closer to zero.
Decimal Numbers Comparison
When dealing with decimals, and especially negative decimals, comparison works just like with whole numbers. But, there's a bit more detail in the way we read them.
Here's how to compare decimal numbers effectively:
  • Align the decimal points vertically.
  • Compare the digits from left to right. Start with the whole number part and move through the decimal places.
  • If the number is negative, remember it is smaller if it is further from zero.
In our example, with -0.59 and -0.52, the numbers align like this:
  • The tenths place is the same, but in the hundredths, 5 is greater than 9.
  • So, we know -0.52 is closer to zero, hence larger than -0.59.
Comparing decimals becomes simpler with these steps and considering their position with respect to zero.

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