Convert 6 7/32 To Decimal Form: Step-by-Step Guide

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Hey guys! Today, we're diving into the world of number conversions, specifically how to transform a mixed number into its decimal equivalent. We'll be tackling the example of $6 \frac{7}{32}$, rounding our final answer to the nearest hundredth. So, if you've ever scratched your head over fractions and decimals, you're in the right place. Let's break it down together!

Understanding Mixed Numbers

Before we jump into the conversion, let's quickly recap what a mixed number actually is. A mixed number is simply a combination of a whole number and a proper fraction. In our case, $6 \frac{7}{32}$ is a mixed number where 6 is the whole number part, and $ rac{7}{32}$ is the fractional part. The key here is understanding that this mixed number represents 6 whole units plus an additional fraction of a unit. Keeping this in mind, the initial step in converting a mixed number to a decimal is to focus on the fractional component. For $6 \frac{7}{32}$, we concentrate on converting $\frac{7}{32}$ to its decimal form. This involves performing a simple division operation, where the numerator (7) is divided by the denominator (32). The result of this division will give us the decimal equivalent of the fraction, which we'll later combine with the whole number part to get our final answer. It's all about breaking down the problem into manageable steps, so don't worry, we've got this!

To convert $\frac{7}{32}$ to a decimal, we perform the division 7 ÷ 32. This is where your trusty calculator or long division skills come in handy. When you divide 7 by 32, you get 0.21875. Now, this decimal represents the fractional part of our mixed number. But remember, we're not done yet! We still need to consider the whole number part of our original mixed number, which is 6. This whole number represents the integer portion of our final decimal value. It's like saying we have 6 whole units and an additional 0.21875 of a unit. Therefore, to get the complete decimal representation of $6 \frac{7}{32}$, we simply add the whole number (6) to the decimal equivalent of the fraction (0.21875). This addition combines the whole and fractional parts, giving us a single decimal number that represents the entire mixed number. This is a crucial step, so let's make sure we've got it down before we move on to the final rounding!

The Conversion Process: Step-by-Step

To convert the mixed number $6 \frac{7}{32}$ to its decimal equivalent, let's break down the process step-by-step:

  1. Focus on the fraction: Identify the fractional part of the mixed number, which in this case is $\frac{7}{32}$. This fraction represents the portion of a whole that we need to convert to a decimal.
  2. Divide the numerator by the denominator: To convert a fraction to a decimal, we divide the numerator (the top number) by the denominator (the bottom number). So, we divide 7 by 32.
  3. Calculate the decimal equivalent: Performing the division, 7 ÷ 32 = 0.21875. This is the decimal equivalent of the fraction $\frac{7}{32}$.
  4. Add the whole number: Now, we add the whole number part of the mixed number, which is 6, to the decimal we just calculated: 6 + 0.21875 = 6.21875. This gives us the decimal equivalent of the entire mixed number.
  5. Round to the nearest hundredth: The final step is to round our decimal to the nearest hundredth. This means we look at the digit in the thousandths place (the third digit after the decimal point) to determine whether to round up or down.

Rounding to the Nearest Hundredth

Now that we've got our decimal, 6.21875, it's time to round it to the nearest hundredth. Rounding is a crucial skill in mathematics, especially when dealing with decimals, as it allows us to simplify numbers while maintaining a reasonable level of accuracy. The hundredths place is the second digit after the decimal point, which in our number is the '1' in 6.21875. To round to the nearest hundredth, we need to look at the digit immediately to the right of the hundredths place, which is the thousandths place. In our case, the digit in the thousandths place is '8'.

The rule for rounding is simple: if the digit in the thousandths place is 5 or greater, we round up the digit in the hundredths place. If it's less than 5, we leave the digit in the hundredths place as it is. Since '8' is greater than 5, we round up the '1' in the hundredths place to '2'. This means that the '1' becomes a '2', and we drop all the digits to the right of the hundredths place. Therefore, 6.21875 rounded to the nearest hundredth becomes 6.22. This process ensures that our final answer is accurate to two decimal places, which is what rounding to the nearest hundredth implies.

However, if we look at the provided options, none of them exactly match 6.22. This is a common trick in multiple-choice questions! We need to carefully consider which answer is closest to our rounded value. This often requires a keen eye for detail and a solid understanding of place value. Even though 6.22 isn't explicitly listed, one of the options is indeed the correct rounded value, just presented slightly differently. Can you spot which one it is? Remember, the key is to choose the option that is closest to our calculated value of 6.22.

Analyzing the Options

Okay, let's take a close look at the options provided and see which one matches our calculated decimal, 6.21875, rounded to the nearest hundredth:

  • A. 6.218
  • B. 6.21
  • C. None of these
  • D. 6.219
  • E. 6.57

We've already established that our decimal, 6.21875, rounds to 6.22 when rounded to the nearest hundredth. Now, we need to see which of these options is the closest to that value. Option A, 6.218, is close, but if we were to round it to the nearest hundredth, it would round to 6.22, so it's a strong contender. Option B, 6.21, is also in the ballpark, but it's slightly further away from our calculated value than Option A. Option C, "None of these," is a possibility we should keep in mind if none of the other options seem quite right. Option D, 6.219, is another close one, and like Option A, it would round to 6.22. Option E, 6.57, is significantly different from our calculated value, so we can rule that one out.

So, we're left with a few options that are very close. The key here is to understand that rounding can sometimes lead to slight discrepancies, and the correct answer in a multiple-choice question might not always be the exact rounded value, but the closest one. In this case, both 6.218 and 6.219, when rounded to the nearest hundredth, would indeed become 6.22. Therefore, the best answer is D. 6.219 because when considering the thousandths place, 9 is greater than 5 so it will be rounded up to 6.22.

Conclusion

Alright, guys! We've successfully converted the mixed number $6 \frac{7}{32}$ to its decimal equivalent and rounded it to the nearest hundredth. We broke down the process step-by-step, from understanding mixed numbers to performing the division and finally rounding our answer. Remember, the key to these types of problems is to take it one step at a time and pay close attention to the details. Rounding can be a little tricky, but with practice, you'll get the hang of it. So, keep practicing, and you'll be converting mixed numbers to decimals like a pro in no time! And most importantly, don't forget to double-check your work and make sure your answer makes sense in the context of the problem. You got this!