Compare And Order Rational Numbers: A Comprehensive Guide

Comparing and ordering rational numbers involves arranging them from least to greatest or vice versa, and COMPARE.EDU.VN provides you with the tools to do just that. Understanding the nuances of rational numbers and their various forms allows for effective comparison and ordering, leading to confident decision-making. Explore techniques for converting fractions, percentages, and square roots into decimals for accurate ordering, and gain insights into applying these methods in real-world scenarios, enabling you to easily perform numerical comparisons.

1. Understanding Rational Numbers

Rational numbers are a fundamental concept in mathematics, and a solid grasp of their definition is crucial for comparing and ordering them effectively.

1.1. What Defines a Rational Number?

A rational number is any number that can be expressed as a fraction (frac{p}{q}), where p and q are integers and q is not equal to zero. The key requirement is that both the numerator (p) and the denominator (q) must be integers, ensuring that the number can be precisely represented as a ratio. This definition encompasses a wide range of numbers, including:

• Integers: Any integer can be written as a fraction with a denominator of 1 (e.g., 5 = (frac{5}{1})).
• Fractions: Numbers expressed in the form (frac{p}{q}) are rational by definition (e.g., (frac{1}{2}), (frac{3}{4}), (frac{-5}{7})).
• Terminating Decimals: Decimals that have a finite number of digits after the decimal point can be converted into fractions (e.g., 0.75 = (frac{3}{4})).
• Repeating Decimals: Decimals with a repeating pattern can also be expressed as fractions (e.g., 0.333… = (frac{1}{3})).

Numbers that cannot be expressed in this form, such as irrational numbers like (sqrt{2}) or π, are not rational numbers. The ability to convert a number into a fraction of integers is what distinguishes rational numbers from irrational numbers.

1.2. Examples of Rational Numbers

To solidify your understanding, let’s look at some specific examples of rational numbers:

• Fractions:

  • (frac{1}{4}): A simple fraction representing one-quarter.
  • (frac{9}{7}): An improper fraction where the numerator is greater than the denominator.
  • (frac{-3}{5}): A negative fraction, still fitting the definition of a rational number.

• Decimals:

  • 0.25: A terminating decimal that is equivalent to (frac{1}{4}).
  • 0.666…: A repeating decimal that is equivalent to (frac{2}{3}).
  • -1.5: A negative terminating decimal that is equivalent to (frac{-3}{2}).

• Percentages:

  • 25%: Can be written as (frac{25}{100}), which simplifies to (frac{1}{4}).
  • 150%: Can be written as (frac{150}{100}), which simplifies to (frac{3}{2}).

• Integers:

  • 5: Can be written as (frac{5}{1}).
  • -3: Can be written as (frac{-3}{1}).
  • 0: Can be written as (frac{0}{1}).

1.3. Why Understanding Rational Numbers Matters

A clear understanding of rational numbers is essential for several reasons:

• Foundation for Advanced Math: Rational numbers are a building block for more complex mathematical concepts, including algebra, calculus, and real analysis.
• Real-World Applications: Rational numbers are used in everyday situations, such as measuring ingredients, calculating proportions, and understanding financial ratios.
• Accurate Comparisons: Knowing how to identify and manipulate rational numbers allows for precise comparisons, whether you’re comparing prices, quantities, or probabilities.

2. Converting Rational Numbers to Decimals

Converting rational numbers to decimal form is a fundamental technique for comparing and ordering them, offering a standardized format that simplifies the process.

2.1. Fractions to Decimals: The Division Method

The most straightforward way to convert a fraction to a decimal is by performing division. Remember that the fraction bar represents division, meaning (frac{p}{q}) is the same as p divided by q. Here’s how to do it:

1. Set up the Long Division: Write the numerator (p) inside the division symbol and the denominator (q) outside.
2. Perform the Division: Divide the numerator by the denominator using long division.
3. Add Decimal and Zeros: If the numerator is smaller than the denominator, add a decimal point and a zero to the numerator to continue the division. Add a decimal point to the quotient (the answer) directly above the decimal point in the dividend.
4. Continue Dividing: Keep adding zeros and dividing until the division terminates (the remainder is zero) or until you reach a repeating pattern.
5. Round if Necessary: If the decimal repeats or continues indefinitely, round it to a suitable number of decimal places for comparison purposes.

Example: Convert (frac{3}{4}) to a decimal.

1. Set up the division: 4 goes into 3.
2. Add a decimal and a zero: 4 goes into 3.0.
3. Divide:
   • 4 goes into 30 seven times (7 x 4 = 28).
   • Subtract 28 from 30, leaving 2.
   • Add another zero: 4 goes into 20.
   • Divide: 4 goes into 20 five times (5 x 4 = 20).
   • Subtract 20 from 20, leaving 0.

So, (frac{3}{4}) = 0.75.

2.2. Percentages to Decimals: Moving the Decimal Point

Converting a percentage to a decimal is a simple process that involves moving the decimal point. Remember that a percentage is a fraction out of 100, so you’re essentially dividing by 100.

1. Remove the Percent Sign: Take away the percent sign (%).
2. Move the Decimal Point: Move the decimal point two places to the left. If there is no visible decimal point, it is assumed to be at the end of the number.

Examples:

• 13%: Remove the percent sign and move the decimal point two places to the left: 0.13.
• 213%: Remove the percent sign and move the decimal point two places to the left: 2.13.
• 5%: Remove the percent sign and move the decimal point two places to the left: 0.05.

2.3. Special Cases: Repeating Decimals

Some fractions, when converted to decimals, result in repeating decimals, where one or more digits repeat indefinitely. For example, (frac{1}{3}) = 0.333…

1. Recognize the Pattern: Identify the repeating digit or sequence of digits.
2. Use Notation: Represent the repeating decimal using a bar over the repeating digits (e.g., 0.333… is written as 0.(bar{3})).
3. Round for Comparison: When comparing or ordering, round the repeating decimal to a suitable number of decimal places. Be consistent with the number of decimal places you use for all numbers in the comparison.

Example: Convert (frac{2}{9}) to a decimal.

1. Divide 2 by 9 using long division.
2. You’ll find that the decimal repeats: 0.222…
3. Write this as 0.(bar{2}).
4. For comparison, round to 0.222 or 0.22, depending on the required precision.

2.4. Tips for Accurate Conversions

• Double-Check Your Work: Division errors can easily occur, so always double-check your calculations.
• Use a Calculator: If permitted, use a calculator to convert fractions to decimals, especially for complex fractions or those with large numbers.
• Maintain Consistency: When comparing multiple numbers, ensure that you round all decimals to the same number of decimal places to avoid inaccuracies.

3. Ordering Rational Numbers: Techniques and Strategies

Once you’ve converted rational numbers into decimals, the next step is to order them from least to greatest or greatest to least. This section outlines effective techniques and strategies for accurately ordering rational numbers.

3.1. Comparing Decimals Directly

The easiest way to order rational numbers is to convert them into decimals and then compare them directly. Follow these steps:

1. Convert All Numbers to Decimals: Use the methods described in the previous section to convert all rational numbers into decimal form.
2. Align Decimal Points: Write the decimals vertically, aligning the decimal points. This ensures that you are comparing the same place values.
3. Compare Digit by Digit: Start comparing the digits from left to right. Begin with the whole number part (the digits to the left of the decimal point). If the whole number parts are different, the number with the smaller whole number is smaller. If the whole number parts are the same, move to the tenths place, then the hundredths place, and so on, until you find a difference.
4. Order the Numbers: Once you have compared all the digits, you can order the numbers from least to greatest or greatest to least, depending on the requirement.

Example: Order the following numbers from least to greatest: 0.35, 0.125, 0.5, 0.08.

1. The numbers are already in decimal form.
2. Align the decimal points:

   0.350
   0.125
   0.500
   0.080

3. Compare digit by digit:
   • The tenths place values are 3, 1, 5, and 0.
   • Ordering these from least to greatest gives us 0, 1, 3, 5.
4. Order the numbers: 0.08, 0.125, 0.35, 0.5.

3.2. Ordering Fractions with Common Denominators

When fractions have the same denominator, comparing them is straightforward:

1. Ensure Common Denominators: If the fractions don’t have the same denominator, find the least common denominator (LCD) and convert each fraction to an equivalent fraction with the LCD.
2. Compare Numerators: Once the denominators are the same, compare the numerators. The fraction with the smaller numerator is smaller.
3. Order the Fractions: Arrange the fractions based on the order of their numerators.

Example: Order the following fractions from least to greatest: (frac{3}{8}), (frac{5}{8}), (frac{1}{8}).

1. The fractions already have a common denominator of 8.
2. Compare the numerators: 1, 3, and 5.
3. Order the fractions: (frac{1}{8}), (frac{3}{8}), (frac{5}{8}).

3.3. Ordering Fractions with Different Denominators

When fractions have different denominators, you need to find a common denominator before comparing them.

1. Find the Least Common Denominator (LCD): Determine the smallest multiple that all the denominators divide into evenly.
2. Convert to Equivalent Fractions: Multiply the numerator and denominator of each fraction by the factor that makes the denominator equal to the LCD.
3. Compare Numerators: Compare the numerators of the equivalent fractions. The fraction with the smaller numerator is smaller.
4. Order the Fractions: Arrange the original fractions based on the order of their numerators in the equivalent fractions.

Example: Order the following fractions from least to greatest: (frac{1}{3}), (frac{1}{4}), (frac{5}{12}).

1. Find the LCD: The LCD of 3, 4, and 12 is 12.
2. Convert to equivalent fractions:
   • (frac{1}{3}) = (frac{1 times 4}{3 times 4}) = (frac{4}{12})
   • (frac{1}{4}) = (frac{1 times 3}{4 times 3}) = (frac{3}{12})
   • (frac{5}{12}) remains (frac{5}{12})
3. Compare the numerators: 3, 4, and 5.
4. Order the fractions: (frac{1}{4}), (frac{1}{3}), (frac{5}{12}).

3.4. Using Benchmarks for Estimation

Benchmarks are common fractions or decimals that can help you quickly estimate the relative size of rational numbers. Common benchmarks include 0, (frac{1}{4}) (0.25), (frac{1}{2}) (0.5), (frac{3}{4}) (0.75), and 1.

1. Compare to Benchmarks: Determine which benchmark each rational number is closest to.
2. Order by Benchmarks: Order the numbers based on their relationship to the benchmarks.
3. Refine as Needed: If numbers are close to the same benchmark, use more precise methods (like converting to decimals) to refine the order.

Example: Order the following numbers from least to greatest: (frac{2}{5}), 0.6, (frac{1}{3}), 0.8.

1. Compare to benchmarks:
   • (frac{2}{5}) is close to (frac{1}{2}) (0.5).
   • 0.6 is slightly greater than (frac{1}{2}) (0.5).
   • (frac{1}{3}) is slightly greater than (frac{1}{4}) (0.25) but less than (frac{1}{2}) (0.5).
   • 0.8 is greater than (frac{3}{4}) (0.75).
2. Order by benchmarks: (frac{1}{3}), (frac{2}{5}), 0.6, 0.8.

3.5. Ordering Mixed Rational Numbers

When dealing with a mix of fractions, decimals, and percentages, the best approach is to convert everything to a single format, usually decimals, and then compare.

1. Convert All to Decimals: Convert all fractions, percentages, and any other formats to decimals.
2. Align Decimal Points: Write the decimals vertically, aligning the decimal points.
3. Compare Digit by Digit: Compare the digits from left to right, starting with the whole number part.
4. Order the Numbers: Arrange the numbers based on the digit-by-digit comparison.
5. Convert Back: If necessary, convert the ordered decimals back to their original forms.

Example: Order the following numbers from least to greatest: 45%, (frac{1}{5}), 0.3, (frac{1}{4}).

1. Convert all to decimals:
   • 45% = 0.45
   • (frac{1}{5}) = 0.2
   • 0.3 = 0.3
   • (frac{1}{4}) = 0.25
2. Align the decimal points:

   0.45
   0.20
   0.30
   0.25

3. Compare digit by digit:
   • The tenths place values are 4, 2, 3, and 2.
   • Ordering these from least to greatest gives us 2, 2, 3, 4.
4. Order the numbers: 0.2, 0.25, 0.3, 0.45.
5. Convert back: (frac{1}{5}), (frac{1}{4}), 0.3, 45%.

3.6. Practical Tips for Ordering

• Use a Number Line: Visualizing numbers on a number line can help you understand their relative positions and make ordering easier.
• Pay Attention to Negative Signs: When ordering negative numbers, remember that the number with the larger absolute value is smaller (e.g., -5 is smaller than -2).
• Be Consistent with Rounding: If you need to round decimals, be consistent with the number of decimal places you use.
• Check Your Answer: After ordering the numbers, double-check your answer to make sure it makes sense.

4. Ordering Square Roots

Ordering square roots can be a bit more challenging, especially when you don’t have a calculator. However, there are effective strategies for estimating and comparing square roots to place them in the correct order.

4.1. Understanding Square Roots

The square root of a number x is a value that, when multiplied by itself, equals x. For example, the square root of 9 is 3 because 3 x 3 = 9. Some numbers have perfect square roots (integers), while others have irrational square roots (non-repeating, non-terminating decimals).

4.2. Identifying Perfect Squares

Knowing perfect squares can greatly simplify the process of estimating square roots. Here are some common perfect squares:

• 1² = 1
• 2² = 4
• 3² = 9
• 4² = 16
• 5² = 25
• 6² = 36
• 7² = 49
• 8² = 64
• 9² = 81
• 10² = 100
• 11² = 121
• 12² = 144
• 13² = 169
• 14² = 196
• 15² = 225

4.3. Estimating Square Roots Without a Calculator

When dealing with square roots that are not perfect squares, you can estimate their values by finding the two perfect squares that the number falls between.

1. Find the Nearest Perfect Squares: Identify the two perfect squares that are closest to the number inside the square root, one smaller and one larger.
2. Determine the Square Roots of the Perfect Squares: Find the square roots of these two perfect squares.
3. Estimate the Square Root: The square root of the original number will fall between the square roots of the two perfect squares. You can estimate its value based on how close the original number is to each perfect square.

Example: Estimate (sqrt{41}).

1. The nearest perfect squares are 36 and 49.
2. (sqrt{36}) = 6 and (sqrt{49}) = 7.
3. Since 41 is closer to 36 than it is to 49, (sqrt{41}) will be slightly greater than 6. A reasonable estimate would be around 6.4.

4.4. Comparing Square Roots

Once you have estimated the square roots, you can compare them to each other and to other rational numbers.

1. Estimate All Square Roots: Use the method described above to estimate the value of each square root.
2. Compare the Estimated Values: Compare the estimated values to determine the order of the square roots.

Example: Order the following numbers from least to greatest: (sqrt{20}), 4, (sqrt{30}), 5.

1. Estimate the square roots:
   • (sqrt{20}): The nearest perfect squares are 16 and 25. (sqrt{16}) = 4 and (sqrt{25}) = 5. Since 20 is closer to 16, (sqrt{20}) is slightly greater than 4 (approximately 4.5).
   • (sqrt{30}): The nearest perfect squares are 25 and 36. (sqrt{25}) = 5 and (sqrt{36}) = 6. Since 30 is closer to 25, (sqrt{30}) is slightly greater than 5 (approximately 5.5).
2. Compare the estimated values: 4, 4.5, 5, 5.5.
3. Order the numbers: 4, (sqrt{20}), 5, (sqrt{30}).

4.5. Tips for Ordering Square Roots

• Memorize Perfect Squares: Knowing the perfect squares up to 15² can significantly speed up the estimation process.
• Use Benchmarks: Use known square roots as benchmarks to help you estimate. For example, (sqrt{4}) = 2, (sqrt{9}) = 3, (sqrt{16}) = 4, and so on.
• Consider the Proximity to Perfect Squares: Pay attention to how close the number inside the square root is to the nearest perfect squares. This will help you refine your estimation.

5. Real-World Applications

Understanding how to Compare And Order Rational Numbers is not just an academic exercise; it has numerous practical applications in everyday life.

5.1. Financial Decisions

When making financial decisions, you often need to compare different interest rates, investment returns, or discounts. These are often expressed as percentages or decimals, and being able to order them accurately is crucial for making informed choices.

• Comparing Interest Rates: When taking out a loan or opening a savings account, you’ll want to compare the interest rates offered by different institutions. For example, if one bank offers an interest rate of 2.5% and another offers 2.75%, you need to be able to determine which is higher.
• Evaluating Investment Returns: When investing, you’ll want to compare the potential returns of different investments. These returns are often expressed as percentages, and being able to order them will help you choose the most profitable option.
• Calculating Discounts: When shopping, you’ll encounter various discounts and sales. Being able to compare different percentage discounts will help you determine which deal is the best. For example, is a 20% discount better than a (frac{1}{4}) off discount?

5.2. Cooking and Baking

Recipes often involve fractions and decimals for measuring ingredients. Being able to compare and order these measurements is essential for accurate cooking and baking.

• Adjusting Recipes: If you need to double or halve a recipe, you’ll need to be able to multiply fractions and decimals accurately. For example, if a recipe calls for (frac{2}{3}) cup of flour and you want to double it, you need to know that (frac{2}{3}) x 2 = (frac{4}{3}) or 1 (frac{1}{3}) cups.
• Comparing Ingredient Quantities: Recipes may list ingredients in different units (e.g., cups, tablespoons, teaspoons). Being able to convert between these units and compare the quantities is crucial for achieving the right balance of flavors.

5.3. Measurement and Construction

In fields like construction, engineering, and design, accurate measurements are essential. These measurements often involve fractions and decimals, and being able to compare and order them is critical for ensuring precision.

• Reading Blueprints: Blueprints often use fractions to represent dimensions. Being able to interpret and compare these fractions is crucial for understanding the design and ensuring that the construction is accurate.
• Cutting Materials: When cutting materials like wood or fabric, you need to be able to measure and compare lengths accurately. This often involves working with fractions of inches or centimeters.

5.4. Data Analysis

In many fields, including science, business, and social sciences, data is often expressed as decimals, percentages, or fractions. Being able to compare and order these values is essential for identifying trends, making inferences, and drawing conclusions.

• Interpreting Statistics: Statistics often involve decimals and percentages. Being able to compare these values is crucial for understanding the data and drawing meaningful conclusions.
• Analyzing Survey Results: Survey results are often expressed as percentages. Being able to compare these percentages is essential for identifying patterns and understanding the opinions of the survey respondents.

6. Common Mistakes to Avoid

When comparing and ordering rational numbers, it’s easy to make mistakes if you’re not careful. Here are some common mistakes to avoid:

6.1. Ignoring Negative Signs

One of the most common mistakes is forgetting to account for negative signs. Remember that negative numbers are always smaller than positive numbers, and the number with the larger absolute value is smaller (e.g., -5 is smaller than -2).

Example: Which is smaller: -0.5 or -0.25?

• Correct: -0.5 is smaller than -0.25 because it is further to the left on the number line.
• Incorrect: Thinking that 0.5 is smaller than 0.25 and applying that to the negative numbers would lead to the wrong answer.

6.2. Incorrectly Converting Fractions to Decimals

Another common mistake is making errors when converting fractions to decimals. This can happen if you perform the division incorrectly or if you round the decimal too early.

Example: Convert (frac{1}{3}) to a decimal.

• Correct: (frac{1}{3}) = 0.333… (repeating).
• Incorrect: Approximating (frac{1}{3}) as 0.3 without recognizing the repeating decimal can lead to inaccuracies when comparing it to other decimals.

6.3. Not Finding a Common Denominator

When comparing fractions with different denominators, it’s essential to find a common denominator before comparing the numerators. Failing to do so can lead to incorrect comparisons.

Example: Which is larger: (frac{2}{5}) or (frac{3}{8})?

• Correct: Find a common denominator (e.g., 40). (frac{2}{5}) = (frac{16}{40}) and (frac{3}{8}) = (frac{15}{40}). Therefore, (frac{2}{5}) is larger than (frac{3}{8}).
• Incorrect: Directly comparing the numerators and denominators without finding a common denominator would lead to the wrong conclusion.

6.4. Rounding Errors

Rounding errors can occur when you round decimals to a certain number of decimal places. If you round too early or inconsistently, you can introduce inaccuracies that affect the final order.

Example: Order the following numbers: 0.333, 0.335, 0.338.

• Correct: 0.333 < 0.335 < 0.338.
• Incorrect: Rounding all the numbers to 0.33 would make them appear equal, leading to an incorrect ordering.

6.5. Misunderstanding Percentages

Percentages can be confusing if you don’t understand what they represent. Remember that a percentage is a fraction out of 100, so you need to divide by 100 to convert it to a decimal.

Example: Which is larger: 50% or 0.6?

• Correct: 50% = 0.5, which is smaller than 0.6.
• Incorrect: Thinking that 50 is larger than 0.6 without converting the percentage to a decimal would lead to the wrong conclusion.

6.6. Ignoring the Context

Sometimes, the context of the problem can provide clues about the relative size of the numbers. Ignoring this context can lead to mistakes.

Example: You are comparing the prices of two items. One item costs $10 with a 10% discount, and the other costs $9 with a 5% discount. Which item is cheaper?

• Correct: Calculating the discounted prices:
  • Item 1: $10 – (10% of $10) = $10 – $1 = $9.
  • Item 2: $9 – (5% of $9) = $9 – $0.45 = $8.55.
  • Therefore, the second item is cheaper.
• Incorrect: Focusing only on the discount percentages (10% vs. 5%) without considering the original prices would lead to the wrong conclusion.

7. Practice Problems

To solidify your understanding of comparing and ordering rational numbers, here are some practice problems:

Problem 1: Order the following numbers from least to greatest: (frac{3}{4}), 0.6, 70%, (frac{2}{3}), 0.75.

Solution:

1. Convert all numbers to decimals:
   • (frac{3}{4}) = 0.75
   • 0.6 = 0.6
   • 70% = 0.7
   • (frac{2}{3}) = 0.666…
   • 0.75 = 0.75
2. Order the decimals: 0.6, 0.666…, 0.7, 0.75, 0.75.
3. Convert back to original form: 0.6, (frac{2}{3}), 70%, (frac{3}{4}), 0.75.

Problem 2: Order the following numbers from greatest to least: -(frac{1}{2}), -0.75, -40%, -(frac{1}{4}), -0.5.

Solution:

1. Convert all numbers to decimals:
   • -(frac{1}{2}) = -0.5
   • -0.75 = -0.75
   • -40% = -0.4
   • -(frac{1}{4}) = -0.25
   • -0.5 = -0.5
2. Order the decimals (remembering that negative numbers are smaller): -0.25, -0.4, -0.5, -0.5, -0.75.
3. Convert back to original form: -(frac{1}{4}), -40%, -(frac{1}{2}), -0.5, -0.75.

Problem 3: Order the following numbers from least to greatest: (sqrt{10}), 3, (sqrt{15}), 4.

Solution:

1. Estimate the square roots:
   • (sqrt{10}): Between (sqrt{9}) = 3 and (sqrt{16}) = 4, closer to 3 (approximately 3.2).
   • (sqrt{15}): Between (sqrt{9}) = 3 and (sqrt{16}) = 4, closer to 4 (approximately 3.9).
2. Order the estimated values: 3, 3.2, 3.9, 4.
3. Convert back to original form: 3, (sqrt{10}), (sqrt{15}), 4.

Problem 4: A store offers three discounts: 20% off, (frac{1}{5}) off, and 0.25 off. Which discount is the best deal?

Solution:

1. Convert all discounts to decimals:
   • 20% = 0.2
   • (frac{1}{5}) = 0.2
   • 0.25 = 0.25
2. Compare the discounts: 0.2, 0.2, 0.25.
3. The best deal is 0.25 off.

Problem 5: You have three savings accounts with interest rates of 1.5%, (frac{3}{200}), and 0.016. Which account has the highest interest rate?

Solution:

1. Convert all interest rates to decimals:
   • 1. 5% = 0.015
   • (frac{3}{200}) = 0.015
   • 0. 016 = 0.016
2. Compare the interest rates: 0.015, 0.015, 0.016.
3. The account with the interest rate of 0.016 has the highest interest rate.

8. Conclusion

Mastering the skill of comparing and ordering rational numbers is essential for various aspects of life, from making informed financial decisions to accurately measuring ingredients in the kitchen. By understanding the definition of rational numbers, learning how to convert between fractions, decimals, and percentages, and practicing effective ordering strategies, you can confidently tackle any numerical comparison challenge. Remember to avoid common mistakes, such as ignoring negative signs or failing to find a common denominator, and always double-check your work to ensure accuracy.

Are you looking for more detailed comparisons and assistance in making informed decisions? Visit COMPARE.EDU.VN today for comprehensive comparisons and expert insights to help you choose the best options for your needs. Our team is dedicated to providing you with the most accurate and up-to-date information, ensuring you can make confident choices every time. Contact us at 333 Comparison Plaza, Choice City, CA 90210, United States or reach out via Whatsapp at +1 (626) 555-9090. Your journey to smarter decisions starts at compare.edu.vn.

9. FAQ

Q1: What is a rational number?

A: A rational number is any number that can be expressed as a fraction (frac{p}{q}), where p and q are integers and q is not equal to zero.

Q2: How do I convert a fraction to a decimal?

A: Divide the numerator by the denominator using long division. Add a decimal point and zeros as needed to continue the division.

Q3: How do I convert a percentage to a decimal?

A: Remove the percent sign and move the decimal point two places to the left.

Q4: What is the least common denominator (LCD)?

A: The LCD is the smallest multiple that all the denominators of a set of fractions divide into evenly.

Q5: How do I compare fractions with different denominators?

A: Find the LCD and convert each fraction to an equivalent fraction with the LCD. Then, compare the numerators.

Q6: How do I estimate the square root of a number without a calculator?

A: Find the two perfect squares that the number falls between. The square root of the original number will fall between the square roots of the two perfect squares.

Q7: What is a repeating decimal?