Comparing Real Numbers Worksheet

Are you a middle school or high school student looking for a reliable resource to improve your understanding of real numbers? If so, this comparing real numbers worksheet is perfect for you! Designed to enhance your knowledge of comparing and ordering real numbers, this worksheet provides ample practice problems that will help reinforce your understanding of this important mathematical concept.

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What is a real number?

A real number is a quantity that represents a value on the number line, including both rational numbers (such as integers and fractions) and irrational numbers (such as pi and square roots). Real numbers can be positive, negative, or zero, and they can be represented as decimals or fractions.

How do you compare two real numbers?

To compare two real numbers, you can simply use the greater than (>), less than (<), equal to (=), greater than or equal to (>=), or less than or equal to (<=) symbols. These symbols will help you determine the relationship between the two numbers based on their respective magnitudes.

What is the symbol for "less than" in comparing real numbers?

The symbol for "less than" in comparing real numbers is "<".

What is the symbol for "greater than" in comparing real numbers?

The symbol for "greater than" in comparing real numbers is ">".

How do you compare fractions as real numbers?

To compare fractions as real numbers, we can convert them to decimals by dividing the numerator by the denominator. The resulting decimal values can then be compared using standard numerical comparison methods such as greater than, less than, or equal to. The fraction with the larger decimal value is considered greater than the other fraction, and the fraction with the smaller decimal value is considered less than the other fraction. If the decimal values are equal, then the fractions are considered equal.

What is the difference between a rational and an irrational number?

A rational number is a number that can be expressed as a ratio of two integers, such as 1/2 or -3/4. On the other hand, an irrational number is a number that cannot be expressed as a simple fraction, such as the square root of 2 or pi. The key difference between the two is that rational numbers can be expressed as fractions, while irrational numbers cannot and have non-repeating, non-terminating decimal expansions.

How can you compare a decimal and a fraction as real numbers?

To compare a decimal and a fraction as real numbers, you can first convert the decimal to a fraction form. This can be done by looking at the decimal places to determine the denominator (10 if there is one decimal place, 100 if two decimal places, and so forth) and then simplifying the fraction. Once both the decimal and fraction are in fraction form, you can compare them by either converting both to decimals for easier comparison or by finding a common denominator and comparing their numerators directly.

How do you compare positive and negative real numbers?

Positive real numbers are greater than zero, while negative real numbers are less than zero. When comparing positive and negative real numbers, any positive real number will always be greater than any negative real number. For example, +5 is greater than -3. Additionally, positive real numbers are always greater than negative real numbers when compared.

How do you compare numbers on a number line?

To compare numbers on a number line, simply look at their positions. The number to the right is always greater than the number to the left. This visual representation makes it easy to see which number is larger or smaller. The greater the distance between two numbers on the number line, the greater the difference between them.

What are the properties of real numbers that help in comparing them?

Real numbers have the properties of being ordered, meaning they can be compared in terms of magnitude (e.g., greater than, less than, or equal to). Real numbers also satisfy the trichotomy property, which states that for any two real numbers a and b, exactly one of the following holds: a < b, a = b, or a > b. These properties make it possible to establish a clear and consistent system of comparison among real numbers.