Which Of The Following Numbers Are Less Than -0.60? Select All That Apply.A. { -\frac{1}{6}$}$B. { -\frac{4}{5}$}$C. { -0.65$}$D. { -0.99$}$
Which of the Following Numbers are Less than -0.60? Select All That Apply
In mathematics, comparing numbers is a fundamental concept that is essential for solving various problems. When dealing with negative numbers, it's crucial to understand the concept of less than and greater than. In this article, we will explore which of the given numbers are less than -0.60. We will analyze each option and provide a detailed explanation of why some numbers are less than -0.60 while others are not.
Before we dive into the comparison, let's briefly review the concept of negative numbers. A negative number is a number that is less than zero. It's denoted by a minus sign (-) preceding the number. For example, -5 is a negative number because it is less than zero.
To compare numbers, we need to determine which number is greater or less than the other. When comparing negative numbers, we can use the following rules:
- If two negative numbers have the same magnitude (i.e., the same absolute value), the number with the smaller exponent (i.e., the number with the smaller negative sign) is greater.
- If two negative numbers have different magnitudes, the number with the smaller magnitude is greater.
Now that we have a basic understanding of negative numbers and comparison, let's analyze each option:
A. {-\frac{1}{6}$}$
To determine if this number is less than -0.60, we need to convert it to a decimal. We can do this by dividing the numerator by the denominator:
Since -0.1667 is greater than -0.60, option A is not less than -0.60.
B. {-\frac{4}{5}$}$
To determine if this number is less than -0.60, we need to convert it to a decimal. We can do this by dividing the numerator by the denominator:
Since -0.8 is greater than -0.60, option B is not less than -0.60.
C. {-0.65$}$
This number is already in decimal form, so we can compare it directly to -0.60. Since -0.65 is less than -0.60, option C is less than -0.60.
D. {-0.99$}$
This number is already in decimal form, so we can compare it directly to -0.60. Since -0.99 is less than -0.60, option D is less than -0.60.
In conclusion, only options C and D are less than -0.60. Option A is greater than -0.60, and option B is also greater than -0.60. Therefore, the correct answer is:
- Option C: {-0.65$}$
- Option D: {-0.99$}$
Comparing numbers is a fundamental concept in mathematics, and understanding negative numbers is crucial for solving various problems. By following the rules for comparing negative numbers, we can determine which numbers are less than or greater than a given number. In this article, we analyzed each option and determined which numbers are less than -0.60. We hope this article has provided a clear understanding of the concept and has helped you in your mathematical journey.
Frequently Asked Questions (FAQs) About Comparing Numbers
In our previous article, we explored which of the given numbers are less than -0.60. We analyzed each option and provided a detailed explanation of why some numbers are less than -0.60 while others are not. In this article, we will answer some frequently asked questions (FAQs) about comparing numbers.
Q: What is the difference between greater than and less than?
A: The difference between greater than and less than is that greater than means a number is larger than another number, while less than means a number is smaller than another number.
Q: How do I compare two negative numbers?
A: To compare two negative numbers, you need to determine which number has the smaller magnitude (i.e., the smaller absolute value). If the magnitudes are the same, you need to compare the exponents (i.e., the negative signs).
Q: What is the rule for comparing negative numbers with different magnitudes?
A: The rule for comparing negative numbers with different magnitudes is that the number with the smaller magnitude is greater.
Q: What is the rule for comparing negative numbers with the same magnitude?
A: The rule for comparing negative numbers with the same magnitude is that the number with the smaller exponent (i.e., the number with the smaller negative sign) is greater.
Q: How do I convert a fraction to a decimal?
A: To convert a fraction to a decimal, you need to divide the numerator by the denominator.
Q: What is the decimal equivalent of {-\frac{1}{6}$}$?
A: The decimal equivalent of {-\frac{1}{6}$}$ is -0.1667.
Q: What is the decimal equivalent of {-\frac{4}{5}$}$?
A: The decimal equivalent of {-\frac{4}{5}$}$ is -0.8.
Q: What is the decimal equivalent of {-0.65$}$?
A: The decimal equivalent of {-0.65$}$ is -0.65.
Q: What is the decimal equivalent of {-0.99$}$?
A: The decimal equivalent of {-0.99$}$ is -0.99.
Q: Which of the following numbers are less than -0.60?
A: The numbers that are less than -0.60 are {-0.65$}$ and {-0.99$}$.
In conclusion, comparing numbers is a fundamental concept in mathematics, and understanding negative numbers is crucial for solving various problems. By following the rules for comparing negative numbers, we can determine which numbers are less than or greater than a given number. We hope this article has provided a clear understanding of the concept and has helped you in your mathematical journey.
Comparing numbers is a skill that is essential for solving various mathematical problems. By practicing and understanding the rules for comparing negative numbers, you can become proficient in this skill and tackle more complex mathematical problems with confidence.