What Is 7/8 As A Decimal? It’s a common question, and what.edu.vn is here to provide a clear, concise answer along with helpful examples. Understanding fraction to decimal conversions simplifies math and everyday calculations. Explore practical applications, fraction simplification, and equivalent fractions, all in one place.
1. Understanding Fractions and Decimals
Fractions and decimals are two different ways of representing parts of a whole. A fraction expresses a part of a whole as a ratio between two numbers: the numerator (the top number) and the denominator (the bottom number). For example, in the fraction 7/8, 7 is the numerator and 8 is the denominator.
A decimal, on the other hand, uses a base-10 system to represent parts of a whole. Decimal numbers are written with a decimal point, where digits to the left of the point represent whole numbers, and digits to the right represent fractions of one, in tenths, hundredths, thousandths, and so on.
Understanding the relationship between fractions and decimals is fundamental in mathematics and has practical applications in everyday life, such as measuring ingredients for cooking, calculating proportions, and understanding financial transactions. Being able to convert between these two forms is a valuable skill that simplifies many calculations and makes it easier to compare different quantities.
2. The Basics of Fraction to Decimal Conversion
Converting a fraction to a decimal involves a simple division. The numerator of the fraction is divided by the denominator. The result of this division is the decimal equivalent of the fraction. This process is straightforward and can be applied to any fraction, making it a versatile tool in various mathematical contexts.
Steps to Convert a Fraction to a Decimal:
- Identify the Numerator and Denominator: Determine which number is on top (numerator) and which is on the bottom (denominator).
- Divide the Numerator by the Denominator: Perform the division. You can use long division, a calculator, or mental math if the numbers are simple enough.
- Write the Result: The result of the division is the decimal equivalent of the fraction.
For example, to convert the fraction 1/2 to a decimal, you would divide 1 (numerator) by 2 (denominator). The result is 0.5, so 1/2 as a decimal is 0.5.
2.1. Why Convert Fractions to Decimals?
Converting fractions to decimals offers several advantages:
- Ease of Comparison: Decimals are easier to compare than fractions. For instance, it’s simpler to see that 0.6 is greater than 0.5 than it is to compare 3/5 and 1/2 directly.
- Simplified Calculations: Many calculations are easier to perform with decimals, especially when using a calculator.
- Standard Representation: Decimals are commonly used in various fields like finance, science, and engineering, making it essential to understand how to convert fractions to decimals.
2.2. Methods for Converting Fractions to Decimals
There are a few methods you can use to convert fractions to decimals:
- Long Division: This is the most common method and involves dividing the numerator by the denominator manually.
- Calculator: Using a calculator is a quick and easy way to convert fractions to decimals. Simply enter the numerator, press the division key, and then enter the denominator.
- Equivalent Fractions with Denominators of 10, 100, 1000, etc.: If you can convert the fraction to an equivalent fraction with a denominator that is a power of 10 (10, 100, 1000, etc.), the conversion to a decimal is straightforward. For example, 1/2 can be converted to 5/10, which is 0.5 as a decimal.
2.3. Common Mistakes to Avoid When Converting Fractions to Decimals
When converting fractions to decimals, be aware of these common mistakes:
- Dividing the Denominator by the Numerator: Always divide the numerator by the denominator, not the other way around.
- Incorrectly Placing the Decimal Point: Make sure to place the decimal point in the correct position after performing the division.
- Rounding Errors: Be careful when rounding decimals, especially in intermediate steps of a calculation, as this can lead to inaccuracies in the final result.
By understanding the basics of fraction to decimal conversion and avoiding common mistakes, you can confidently convert fractions to decimals and use them in various mathematical and practical contexts.
3. Converting 7/8 to a Decimal: Step-by-Step
Converting 7/8 to a decimal involves dividing the numerator (7) by the denominator (8). Here’s a step-by-step guide on how to do it:
- Set up the Division: Write the division problem as 7 ÷ 8.
- Perform Long Division:
- Since 8 doesn’t go into 7, add a decimal point and a zero to 7, making it 7.0.
- 8 goes into 70 eight times (8 x 8 = 64). Write 8 after the decimal point in the quotient.
- Subtract 64 from 70, which leaves a remainder of 6.
- Add another zero to the remainder, making it 60.
- 8 goes into 60 seven times (8 x 7 = 56). Write 7 after 8 in the quotient.
- Subtract 56 from 60, which leaves a remainder of 4.
- Add another zero to the remainder, making it 40.
- 8 goes into 40 five times (8 x 5 = 40). Write 5 after 7 in the quotient.
- Subtract 40 from 40, which leaves a remainder of 0.
- Write the Result: The result of the division is 0.875.
Therefore, 7/8 as a decimal is 0.875.
3.1. Using a Calculator to Convert 7/8 to a Decimal
You can also use a calculator to convert 7/8 to a decimal:
- Enter 7 into the calculator.
- Press the division key (÷).
- Enter 8 into the calculator.
- Press the equals key (=).
The calculator will display 0.875.
3.2. Understanding the Decimal Value of 7/8
The decimal value of 7/8, which is 0.875, represents that 7/8 is slightly more than 3/4 (0.75) but less than 1 (1.0). In practical terms, if you have a pie divided into 8 slices and you take 7 of those slices, you have 0.875 or 87.5% of the pie.
4. Practical Applications of 7/8 as a Decimal
Understanding 7/8 as a decimal (0.875) has numerous practical applications in various fields. Here are a few examples:
- Cooking and Baking:
- In recipes, measurements are often given in fractions. Knowing the decimal equivalent of 7/8 helps in accurately measuring ingredients. For instance, if a recipe calls for 7/8 cup of flour, you can measure 0.875 cup using a measuring cup with decimal markings.
- Construction and Carpentry:
- In construction and carpentry, precise measurements are crucial. If a plan requires cutting a piece of wood to 7/8 inch, using the decimal equivalent (0.875 inch) ensures accuracy.
- Engineering:
- Engineers often work with precise calculations involving fractions. Converting 7/8 to 0.875 allows for easier integration into complex equations and simulations.
- Finance:
- Understanding fractions and decimals is essential in finance for calculating interest rates, percentages, and proportions. For example, if an investment yields 7/8 of a percent interest, knowing it is 0.875% helps in accurate financial planning.
- Academic Settings:
- Students often encounter fractions in math and science problems. Converting fractions to decimals simplifies calculations and makes problem-solving more efficient.
- Everyday Life:
- Splitting a bill: If you need to divide a cost where one person pays 7/8 of the total, converting to 0.875 makes the calculation easier.
4.1. Example Scenarios
Here are a few scenarios illustrating the practical use of 7/8 as a decimal:
- Scenario 1: Baking a Cake
- A cake recipe requires 7/8 cup of sugar. Using a measuring cup with decimal markings, you measure 0.875 cup of sugar to ensure the cake turns out perfectly.
- Scenario 2: Building a Bookshelf
- You need to cut a shelf to be exactly 7/8 inch thick. Using a ruler with decimal markings, you measure 0.875 inch to cut the wood accurately.
- Scenario 3: Calculating Investment Returns
- An investment promises a return of 7/8 percent annually. To calculate the actual return on a $10,000 investment, you multiply $10,000 by 0.00875 (the decimal equivalent of 0.875%), resulting in a return of $87.50.
- Scenario 4: Dividing Expenses
- You and a friend agree that you will cover 7/8 of the expenses for a project. If the total expenses are $200, you calculate that you need to pay 0.875 * $200 = $175.
4.2. Real-World Measurements
In many real-world applications, measurements are often expressed in fractions. Here are some examples:
- Inch Fractions: Measurements in inches are commonly expressed as fractions, such as 1/2 inch, 1/4 inch, 1/8 inch, and so on. Knowing the decimal equivalents of these fractions is essential for accurate measurements.
- Volume Measurements: In cooking and baking, volume measurements like cups and tablespoons are often expressed as fractions.
- Liquid Measurements: In chemistry and other scientific fields, liquid measurements are often expressed as fractions of a liter or milliliter.
By understanding 7/8 as a decimal and how to apply it in these practical scenarios, you can improve accuracy and efficiency in various tasks and professions.
5. Converting Other Fractions to Decimals
Converting other fractions to decimals follows the same basic principle as converting 7/8 to a decimal. The key is to divide the numerator by the denominator. Here are a few examples:
5.1. Converting 1/4 to a Decimal
To convert 1/4 to a decimal, divide 1 by 4:
1 ÷ 4 = 0.25
Therefore, 1/4 as a decimal is 0.25.
5.2. Converting 1/2 to a Decimal
To convert 1/2 to a decimal, divide 1 by 2:
1 ÷ 2 = 0.5
Therefore, 1/2 as a decimal is 0.5.
5.3. Converting 3/4 to a Decimal
To convert 3/4 to a decimal, divide 3 by 4:
3 ÷ 4 = 0.75
Therefore, 3/4 as a decimal is 0.75.
5.4. Converting 1/3 to a Decimal
To convert 1/3 to a decimal, divide 1 by 3:
1 ÷ 3 = 0.3333…
Therefore, 1/3 as a decimal is approximately 0.333. This is a repeating decimal, meaning the digit 3 repeats infinitely. In such cases, it is common to round the decimal to a certain number of decimal places.
5.5. Converting 2/3 to a Decimal
To convert 2/3 to a decimal, divide 2 by 3:
2 ÷ 3 = 0.6666…
Therefore, 2/3 as a decimal is approximately 0.667. This is also a repeating decimal, and it is rounded to three decimal places.
5.6. Converting 5/8 to a Decimal
To convert 5/8 to a decimal, divide 5 by 8:
5 ÷ 8 = 0.625
Therefore, 5/8 as a decimal is 0.625.
5.7. Quick Reference Table
Here’s a quick reference table for some common fractions and their decimal equivalents:
| Fraction | Decimal Equivalent |
|---|---|
| 1/4 | 0.25 |
| 1/2 | 0.5 |
| 3/4 | 0.75 |
| 1/3 | 0.333 (approx.) |
| 2/3 | 0.667 (approx.) |
| 1/8 | 0.125 |
| 3/8 | 0.375 |
| 5/8 | 0.625 |
| 7/8 | 0.875 |
6. Understanding Decimal Place Values
Understanding decimal place values is essential for accurately working with decimals. Each digit in a decimal number has a specific place value, which determines its contribution to the overall value of the number.
6.1. Decimal Place Value Chart
Here is a decimal place value chart:
| Place Value | Value | Example (in 123.456) |
|---|---|---|
| Hundreds | 100 | 1 |
| Tens | 10 | 2 |
| Ones | 1 | 3 |
| Decimal Point | . | . |
| Tenths | 1/10 (0.1) | 4 |
| Hundredths | 1/100 (0.01) | 5 |
| Thousandths | 1/1000 (0.001) | 6 |
In the number 123.456:
- 1 is in the hundreds place, so it represents 100.
- 2 is in the tens place, so it represents 20.
- 3 is in the ones place, so it represents 3.
- 4 is in the tenths place, so it represents 0.4.
- 5 is in the hundredths place, so it represents 0.05.
- 6 is in the thousandths place, so it represents 0.006.
6.2. Significance of Decimal Places
The number of decimal places indicates the precision of a measurement or calculation. The more decimal places, the more accurate the value. For example:
- 0.8 is accurate to the nearest tenth.
- 0.87 is accurate to the nearest hundredth.
- 0.875 is accurate to the nearest thousandth.
6.3. Rounding Decimals
Rounding decimals involves reducing the number of decimal places while keeping the value as close as possible to the original number. Here are the basic rules for rounding:
- Identify the Digit to Round: Determine the decimal place to which you want to round.
- Look at the Next Digit to the Right:
- If the next digit is 5 or greater, round up (add 1 to the digit you are rounding).
- If the next digit is less than 5, round down (keep the digit you are rounding as it is).
- Drop the Digits to the Right: Remove all digits to the right of the rounded digit.
For example:
- Rounding 0.875 to the nearest hundredth:
- The digit in the hundredths place is 7.
- The next digit to the right is 5, so round up.
-
- 875 rounded to the nearest hundredth is 0.88.
- Rounding 0.875 to the nearest tenth:
- The digit in the tenths place is 8.
- The next digit to the right is 7, so round up.
-
- 875 rounded to the nearest tenth is 0.9.
6.4. Common Rounding Scenarios
- Money: In financial calculations, amounts are often rounded to the nearest cent (two decimal places).
- Science: In scientific measurements, the number of decimal places is determined by the precision of the measuring instrument.
- Engineering: Engineers often use specific rounding rules to ensure accuracy and consistency in calculations.
Understanding decimal place values and rounding rules is crucial for accurate calculations and measurements in various fields.
7. The Relationship Between Fractions, Decimals, and Percentages
Fractions, decimals, and percentages are three different ways of representing the same value, each with its own advantages and applications. Understanding the relationship between them is essential for mathematical proficiency.
7.1. Converting Fractions to Percentages
To convert a fraction to a percentage, first convert the fraction to a decimal, and then multiply the decimal by 100. The result is the percentage equivalent of the fraction.
Steps to Convert a Fraction to a Percentage:
- Convert the Fraction to a Decimal: Divide the numerator by the denominator.
- Multiply the Decimal by 100: Multiply the result by 100 to express it as a percentage.
- Add the Percent Sign (%): Add the percent sign to the end of the number.
For example, to convert 7/8 to a percentage:
- Convert 7/8 to a decimal: 7 ÷ 8 = 0.875
- Multiply the decimal by 100: 0.875 x 100 = 87.5
- Add the percent sign: 87.5%
Therefore, 7/8 as a percentage is 87.5%.
7.2. Converting Decimals to Percentages
To convert a decimal to a percentage, simply multiply the decimal by 100 and add the percent sign.
Steps to Convert a Decimal to a Percentage:
- Multiply the Decimal by 100: Multiply the decimal by 100 to express it as a percentage.
- Add the Percent Sign (%): Add the percent sign to the end of the number.
For example, to convert 0.875 to a percentage:
- Multiply the decimal by 100: 0.875 x 100 = 87.5
- Add the percent sign: 87.5%
Therefore, 0.875 as a percentage is 87.5%.
7.3. Converting Percentages to Fractions
To convert a percentage to a fraction, divide the percentage by 100 and simplify the resulting fraction.
Steps to Convert a Percentage to a Fraction:
- Divide the Percentage by 100: Divide the percentage by 100 to express it as a decimal.
- Convert the Decimal to a Fraction: Write the decimal as a fraction with a denominator of 10, 100, 1000, etc., depending on the number of decimal places.
- Simplify the Fraction: Simplify the fraction to its lowest terms.
For example, to convert 87.5% to a fraction:
- Divide the percentage by 100: 87.5 ÷ 100 = 0.875
- Convert the decimal to a fraction: 0.875 = 875/1000
- Simplify the fraction: 875/1000 = 7/8
Therefore, 87.5% as a fraction is 7/8.
7.4. Practical Examples
- Calculating Discounts: If an item is 25% off, you can convert 25% to a decimal (0.25) or a fraction (1/4) to calculate the discount amount.
- Understanding Test Scores: If you score 80% on a test, you can convert 80% to a decimal (0.8) or a fraction (4/5) to understand your performance relative to the total possible score.
- Financial Planning: When calculating interest rates or investment returns, it is often necessary to convert percentages to decimals or fractions to perform accurate calculations.
7.5. Quick Conversion Table
Here is a quick conversion table for some common values:
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/4 | 0.25 | 25% |
| 1/2 | 0.5 | 50% |
| 3/4 | 0.75 | 75% |
| 1/3 | 0.333 | 33.3% |
| 2/3 | 0.667 | 66.7% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
By understanding the relationship between fractions, decimals, and percentages, you can easily convert between these forms and apply them in various mathematical and practical contexts.
8. Common Fractions and Their Decimal Equivalents
Knowing the decimal equivalents of common fractions can save time and effort in many calculations. Here is a list of common fractions and their decimal equivalents:
| Fraction | Decimal Equivalent |
|---|---|
| 1/2 | 0.5 |
| 1/3 | 0.333… |
| 2/3 | 0.666… |
| 1/4 | 0.25 |
| 3/4 | 0.75 |
| 1/5 | 0.2 |
| 2/5 | 0.4 |
| 3/5 | 0.6 |
| 4/5 | 0.8 |
| 1/8 | 0.125 |
| 3/8 | 0.375 |
| 5/8 | 0.625 |
| 7/8 | 0.875 |
| 1/10 | 0.1 |
| 1/100 | 0.01 |
8.1. Fractions with Repeating Decimal Equivalents
Some fractions, like 1/3 and 2/3, have decimal equivalents that are repeating decimals. A repeating decimal is a decimal in which one or more digits repeat infinitely. In the case of 1/3, the decimal equivalent is 0.333…, and in the case of 2/3, the decimal equivalent is 0.666….
When working with repeating decimals, it is often necessary to round the decimal to a certain number of decimal places. The number of decimal places to which you round depends on the level of precision required for the calculation.
8.2. Fractions with Terminating Decimal Equivalents
Other fractions, like 1/2, 1/4, and 1/5, have decimal equivalents that are terminating decimals. A terminating decimal is a decimal that has a finite number of digits. For example, 1/2 has a decimal equivalent of 0.5, which has only one digit after the decimal point.
8.3. Tips for Memorizing Common Fraction-Decimal Equivalents
Memorizing common fraction-decimal equivalents can be helpful in various situations. Here are a few tips for memorizing these equivalents:
- Use Flashcards: Create flashcards with the fraction on one side and the decimal equivalent on the other side. Practice with the flashcards regularly to reinforce your memory.
- Practice with Examples: Work through examples that involve converting fractions to decimals and vice versa. The more you practice, the better you will remember the equivalents.
- Look for Patterns: Look for patterns in the equivalents. For example, notice that fractions with a denominator of 8 all have decimal equivalents that end in .125, .375, .625, or .875.
- Use Real-World Examples: Relate the fractions and decimals to real-world examples. For example, think of 1/2 as half of something, and 0.5 as 50%.
9. Understanding Equivalent Fractions
Equivalent fractions are fractions that represent the same value, even though they have different numerators and denominators. Understanding equivalent fractions is essential for simplifying fractions and performing calculations involving fractions.
9.1. What are Equivalent Fractions?
Equivalent fractions are fractions that are equal in value but have different numerators and denominators. For example, 1/2 and 2/4 are equivalent fractions because they both represent the same value (0.5).
9.2. How to Find Equivalent Fractions
To find equivalent fractions, you can multiply or divide both the numerator and the denominator of a fraction by the same non-zero number. This does not change the value of the fraction, but it does change the numerator and denominator.
Steps to Find Equivalent Fractions:
- Choose a Number: Choose any non-zero number.
- Multiply or Divide: Multiply or divide both the numerator and the denominator of the fraction by the chosen number.
- Write the Equivalent Fraction: The resulting fraction is an equivalent fraction.
For example, to find an equivalent fraction for 1/2:
- Choose the number 2.
- Multiply both the numerator and the denominator by 2: (1 x 2) / (2 x 2) = 2/4
- The equivalent fraction is 2/4.
9.3. Simplifying Fractions
Simplifying a fraction involves reducing it to its lowest terms. This means finding an equivalent fraction with the smallest possible numerator and denominator. To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD).
Steps to Simplify a Fraction:
- Find the GCD: Find the greatest common divisor (GCD) of the numerator and the denominator.
- Divide by the GCD: Divide both the numerator and the denominator by the GCD.
- Write the Simplified Fraction: The resulting fraction is the simplified fraction.
For example, to simplify the fraction 4/8:
- Find the GCD of 4 and 8: The GCD is 4.
- Divide both the numerator and the denominator by 4: (4 ÷ 4) / (8 ÷ 4) = 1/2
- The simplified fraction is 1/2.
9.4. Cross-Multiplication
Cross-multiplication is a technique used to determine whether two fractions are equivalent. To cross-multiply, multiply the numerator of the first fraction by the denominator of the second fraction, and multiply the numerator of the second fraction by the denominator of the first fraction. If the two products are equal, then the fractions are equivalent.
Steps to Cross-Multiply:
- Write the Fractions: Write the two fractions that you want to compare.
- Cross-Multiply: Multiply the numerator of the first fraction by the denominator of the second fraction, and multiply the numerator of the second fraction by the denominator of the first fraction.
- Compare the Products: Compare the two products. If the products are equal, then the fractions are equivalent.
For example, to determine whether 1/2 and 2/4 are equivalent:
- Write the fractions: 1/2 and 2/4
- Cross-multiply: (1 x 4) = 4 and (2 x 2) = 4
- Compare the products: Since 4 = 4, the fractions are equivalent.
Understanding equivalent fractions, simplifying fractions, and cross-multiplication are essential skills for working with fractions and solving mathematical problems.
10. Complex Fractions and Decimal Conversion
Complex fractions are fractions that have a fraction in the numerator, the denominator, or both. Converting complex fractions to decimals involves simplifying the complex fraction first and then converting the resulting simple fraction to a decimal.
10.1. What are Complex Fractions?
A complex fraction is a fraction where the numerator, the denominator, or both contain a fraction. For example:
- (1/2) / 3
- 2 / (3/4)
- (1/2) / (3/4)
10.2. Simplifying Complex Fractions
To simplify a complex fraction, you can use one of two methods:
- Method 1: Combining Fractions
- Simplify the numerator and the denominator separately.
- Divide the simplified numerator by the simplified denominator.
- Method 2: Multiplying by the Reciprocal
- Multiply the numerator by the reciprocal of the denominator.
Example 1: Simplifying (1/2) / 3
- Using Method 1:
- The numerator is 1/2.
- The denominator is 3.
- Divide the numerator by the denominator: (1/2) ÷ 3 = (1/2) x (1/3) = 1/6
- Using Method 2:
- The numerator is 1/2.
- The denominator is 3.
- Multiply the numerator by the reciprocal of the denominator: (1/2) x (1/3) = 1/6
- The simplified fraction is 1/6.
Example 2: Simplifying 2 / (3/4)
- Using Method 1:
- The numerator is 2.
- The denominator is 3/4.
- Divide the numerator by the denominator: 2 ÷ (3/4) = 2 x (4/3) = 8/3
- Using Method 2:
- The numerator is 2.
- The denominator is 3/4.
- Multiply the numerator by the reciprocal of the denominator: 2 x (4/3) = 8/3
- The simplified fraction is 8/3.
Example 3: Simplifying (1/2) / (3/4)
- Using Method 1:
- The numerator is 1/2.
- The denominator is 3/4.
- Divide the numerator by the denominator: (1/2) ÷ (3/4) = (1/2) x (4/3) = 4/6 = 2/3
- Using Method 2:
- The numerator is 1/2.
- The denominator is 3/4.
- Multiply the numerator by the reciprocal of the denominator: (1/2) x (4/3) = 4/6 = 2/3
- The simplified fraction is 2/3.
10.3. Converting Simplified Fractions to Decimals
Once you have simplified the complex fraction to a simple fraction, you can convert it to a decimal by dividing the numerator by the denominator, as described in previous sections.
Example 1: Converting 1/6 to a Decimal
- Divide the numerator (1) by the denominator (6): 1 ÷ 6 = 0.1666…
- The decimal equivalent is approximately 0.167.
Example 2: Converting 8/3 to a Decimal
- Divide the numerator (8) by the denominator (3): 8 ÷ 3 = 2.666…
- The decimal equivalent is approximately 2.667.
Example 3: Converting 2/3 to a Decimal
- Divide the numerator (2) by the denominator (3): 2 ÷ 3 = 0.666…
- The decimal equivalent is approximately 0.667.
10.4. Practical Applications
Complex fractions can appear in various mathematical problems and real-world scenarios. Being able to simplify them and convert them to decimals is a valuable skill. For example:
- Physics: In physics, complex fractions may be used in calculations involving rates, ratios, and proportions.
- Engineering: Engineers may encounter complex fractions in various calculations related to design and analysis.
- Finance: Complex fractions may be used in financial calculations involving investments, returns, and interest rates.
11. Advanced Techniques for Fraction and Decimal Manipulation
Mastering fraction and decimal manipulation involves understanding more advanced techniques. These techniques can help you solve complex problems more efficiently and accurately.
11.1. Converting Repeating Decimals to Fractions
Converting repeating decimals to fractions involves a specific algebraic technique. Here’s how to do it:
- Assign a Variable: Let x equal the repeating decimal.
- Multiply by a Power of 10: Multiply x by a power of 10 that moves the repeating part to the left of the decimal point.
- Subtract the Original Equation: Subtract the original equation (x = repeating decimal) from the new equation.
- Solve for x: Solve the resulting equation for x.
- Simplify the Fraction: Simplify the fraction if possible.
Example: Convert 0.333… to a Fraction
- Let x = 0.333…
- Multiply by 10: 10x = 3.333…
- Subtract the original equation: 10x – x = 3.333… – 0.333… => 9x = 3
- Solve for x: x = 3/9
- Simplify the fraction: x = 1/3
Therefore, 0.333… as a fraction is 1/3.
Example: Convert 0.121212… to a Fraction
- Let x = 0.121212…
- Multiply by 100: 100x = 12.121212…
- Subtract the original equation: 100x – x = 12.121212… – 0.121212… => 99x = 12
- Solve for x: x = 12/99
- Simplify the fraction: x = 4
