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Chapter 1: Problem 50

Write a true sentence using either \(< or >\) $$ -10.3 \square-14.5 $$

Short Answer

Expert verified
-10.3 > -14.5.

Step by step solution

01

Understand the comparison

Determine which of the two numbers, -10.3 and -14.5, is greater or smaller.
02

Compare the two numbers

On a number line, every number to the right is greater. Here, -10.3 is closer to zero compared to -14.5.
03

Conclusion

Since -10.3 is closer to zero, it is greater than -14.5. Therefore the statement should use >.
04

Write the sentence

The true sentence using either < or > is -10.3 > -14.5.

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Key Concepts

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

number line
A number line is a visual representation of numbers laid out in a straight, horizontal line. Every point on this line represents a number.
The line is usually drawn with zero in the middle, with positive numbers to the right and negative numbers to the left.
Here are some key points to remember about the number line:
  • Numbers to the right are always greater than numbers to the left.
  • Negative numbers are always on the left side of zero, getting smaller as they move further left.
  • Positive numbers are on the right side of zero and increase as they move further right.
Using a number line, you can visually compare -10.3 and -14.5. Since -10.3 is to the right of -14.5, \(-10.3 > -14.5\).
greater than
When we say one number is *greater than* another, it means the first number is larger.
In other words, it is to the right of the other number on the number line.
To compare -10.3 and -14.5, remember these points:
  • If a number is closer to zero on the number line, it is greater than another number that is further away from zero.
  • Thus, -10.3 is greater than -14.5 because it is closer to zero.
  • The symbol \(>\) is used to denote 'greater than'
Therefore, we write: \(-10.3 > -14.5\).
less than
When we say one number is *less than* another, it means the first number is smaller.
To determine whether a number is less than another, you can use these points:
  • If a number is further to the left on the number line, it is less than a number that is to the right.
  • Negative numbers are less than positive numbers.
  • A smaller negative number is one that is further away from zero and more towards the left.
With -10.3 and -14.5, if you think using 'less than,' it makes sense to say -14.5 is less than -10.3:
\(-14.5 < -10.3\).
negative values
Negative values are numbers less than zero.
These numbers are found to the left of zero on the number line, and the further left they are, the smaller they are in value.
Important points about negative values include:
  • Negative numbers are always less than positive numbers.
  • The closer a negative number is to zero, the larger its value is.
  • Examples: -1 is greater than -2, and -10.3 is greater than -14.5.
When comparing -10.3 and -14.5, -10.3 is a larger (greater) negative value because it is closer to zero. So we write:
\(-10.3 > -14.5\).

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Most popular questions from this chapter

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