Converting Fractions To Decimals: A Step-by-Step Guide

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Hey guys! Today, we're going to dive into the world of fractions and decimals. Specifically, we'll learn how to convert common fractions into decimal fractions and round the answers to the nearest hundredth. This is a fundamental skill in mathematics, and it's super useful in everyday life, from cooking to measuring to understanding financial figures. So, grab your pencils and let's get started!

Understanding Fractions and Decimals

Before we jump into the conversion process, let's quickly recap what fractions and decimals are. Think of a fraction as a way to represent a part of a whole. It consists of two numbers: the numerator (the top number) and the denominator (the bottom number). The numerator tells you how many parts you have, and the denominator tells you how many parts the whole is divided into. For example, in the fraction 1/2, the numerator is 1, and the denominator is 2. This means you have one part out of a total of two parts.

Decimals, on the other hand, are another way to represent parts of a whole, but they use a base-10 system. This means each digit in a decimal number represents a power of 10. The digits to the right of the decimal point represent fractions with denominators that are powers of 10 (e.g., 0.1 is 1/10, 0.01 is 1/100, 0.001 is 1/1000, and so on). Understanding this relationship between fractions and decimals is key to converting between the two.

The Conversion Process: Fractions to Decimals

The main method for converting a fraction to a decimal is through division. You simply divide the numerator (the top number) by the denominator (the bottom number). The result will be the decimal equivalent of the fraction.

Let's look at some examples to make this clear:

Example 1: Converting 12/13 to a Decimal

To convert 12/13 to a decimal, we'll divide 12 by 13. You can use a calculator for this, or you can do long division if you're feeling old-school. When you divide 12 by 13, you get approximately 0.9230769... Since we need to round to the nearest hundredth, we look at the first two digits after the decimal point, which are 92 (0.92). Then we look at the third digit, which is 3. Because 3 is less than 5, we round down. So, 12/13 rounded to the nearest hundredth is approximately 0.92.

  • Step 1: Divide the numerator by the denominator: 12 ÷ 13 ≈ 0.9230769
  • Step 2: Identify the hundredths place: The hundredths place is the second digit after the decimal point (2 in this case).
  • Step 3: Look at the next digit (the thousandths place): The digit in the thousandths place is 3.
  • Step 4: Round: Since 3 is less than 5, we round down and keep the hundredths digit as it is. Therefore, 12/13 ≈ 0.92.

Example 2: Converting 42/17 to a Decimal

To convert 42/17 to a decimal, we divide 42 by 17. This gives us approximately 2.4705882... Rounding to the nearest hundredth means we look at the 7 in the hundredths place. The next digit is 0, which is less than 5, so we round down. Therefore, 42/17 rounded to the nearest hundredth is approximately 2.47.

  • Step 1: Divide: 42 ÷ 17 ≈ 2.4705882
  • Step 2: Hundredths place: 7
  • Step 3: Thousandths place: 0
  • Step 4: Round: 2.47

Example 3: Converting 19/21 to a Decimal

For 19/21, divide 19 by 21, and you'll get approximately 0.9047619... To round to the nearest hundredth, focus on the 0 in the hundredths place. The next digit is 4, so we round down. The result is approximately 0.90.

  • Step 1: Divide: 19 ÷ 21 ≈ 0.9047619
  • Step 2: Hundredths place: 0
  • Step 3: Thousandths place: 4
  • Step 4: Round: 0.90

Example 4: Converting 74/15 to a Decimal

Now, let's convert 74/15 to a decimal. Dividing 74 by 15 gives us approximately 4.9333333... The hundredths digit is 3, and the next digit is also 3. Since 3 is less than 5, we round down, so the result is approximately 4.93.

  • Step 1: Divide: 74 ÷ 15 ≈ 4.9333333
  • Step 2: Hundredths place: 3
  • Step 3: Thousandths place: 3
  • Step 4: Round: 4.93

Example 5: Converting a Mixed Fraction 5 8/11 to a Decimal

Converting mixed fractions requires an extra step. First, focus on the fractional part (8/11). Divide 8 by 11, which gives you approximately 0.7272727... Now, add the whole number part (5) to this decimal. So, 5 + 0.7272727... = 5.7272727... Rounding to the nearest hundredth, we look at the hundredths digit, which is 2. The next digit is 7, which is greater than or equal to 5, so we round up. The result is approximately 5.73.

  • Step 1: Convert the fractional part (8/11): 8 ÷ 11 ≈ 0.7272727
  • Step 2: Add the whole number: 5 + 0.7272727 ≈ 5.7272727
  • Step 3: Hundredths place: 2
  • Step 4: Thousandths place: 7
  • Step 5: Round: 5.73

Example 6: Converting a Mixed Fraction 2 11/23 to a Decimal

Let's tackle another mixed fraction. To convert 2 11/23 to a decimal, we'll first convert the fraction 11/23 by dividing 11 by 23, which is approximately 0.4782608... Then, we add the whole number 2, so we have 2 + 0.4782608... = 2.4782608... Rounding to the nearest hundredth, we look at the 7 in the hundredths place. The next digit is 8, which is greater than or equal to 5, so we round up. The result is approximately 2.48.

  • Step 1: Convert the fractional part (11/23): 11 ÷ 23 ≈ 0.4782608
  • Step 2: Add the whole number: 2 + 0.4782608 ≈ 2.4782608
  • Step 3: Hundredths place: 7
  • Step 4: Thousandths place: 8
  • Step 5: Round: 2.48

Rounding to the Nearest Hundredth: A Quick Guide

Rounding to the nearest hundredth is a crucial step in this process. Here’s a quick reminder of the rules:

  • Identify the Hundredths Place: This is the second digit to the right of the decimal point.
  • Look at the Next Digit (Thousandths Place): If this digit is 5 or greater, round up the hundredths digit. If it's 4 or less, round down (keep the hundredths digit as it is).

Solving Word Problems Involving Fraction to Decimal Conversions

Now that we know how to convert fractions to decimals, let’s think about how this applies to real-world problems. Word problems often require you to convert fractions to decimals to perform calculations or make comparisons. Identifying the relevant information and setting up the problem correctly is key.

Tips for Solving Word Problems

  1. Read the problem carefully: Understand what the problem is asking before you start trying to solve it.
  2. Identify key information: Look for fractions or situations where you might need to convert a fraction to a decimal.
  3. Set up the equation: Determine what operation(s) you need to perform (addition, subtraction, multiplication, division).
  4. Solve the problem: Perform the calculations, remembering to round if necessary.
  5. Check your answer: Does your answer make sense in the context of the problem?

Practice Makes Perfect

Like any math skill, converting fractions to decimals becomes easier with practice. Work through plenty of examples, and don't be afraid to use a calculator to check your work. The more you practice, the more confident you'll become!

Conclusion

So, there you have it! Converting fractions to decimals is a straightforward process once you understand the basic principle of dividing the numerator by the denominator. Remember to round your answers appropriately, especially when dealing with real-world applications. With a little practice, you'll be a pro at converting fractions to decimals in no time. Keep up the great work, guys, and happy converting!