Decimal Calculation: 2.11 X 2 7/16 Explained

Hey guys! Today, we're diving into a math problem that involves decimal calculations and mixed numbers. Specifically, we're going to tackle the question of how to calculate 2.11 multiplied by 2 7/16 in decimal form, making sure to round our answer correctly. It might sound a bit tricky at first, but don't worry, we'll break it down step by step so it's super easy to understand. Let's get started!

Understanding the Problem

Before we jump into the calculation, let's make sure we understand what the problem is asking. We need to multiply a decimal number (2.11) by a mixed number (2 7/16). To do this effectively, we'll first need to convert the mixed number into a decimal. This will allow us to perform the multiplication seamlessly. Then, we'll focus on rounding the result to match the number of decimal places in our original decimal number, 2.11. This means we are aiming for an answer with two decimal places. Understanding this is crucial because the precision of our answer is just as important as the answer itself. So, keep in mind, our goal is not just to find the product, but to present it in the correct format, adhering to the rules of decimal representation and rounding. This ensures our answer is both accurate and clearly communicated.

Converting Mixed Numbers to Decimals

The first key step in solving this problem is converting the mixed number, 2 7/16, into a decimal. To do this, we need to understand what a mixed number represents. A mixed number is a combination of a whole number and a fraction. In our case, 2 7/16 means we have two whole units and an additional 7/16 of a unit. The whole number part is already in a decimal format (it's simply 2), but we need to convert the fractional part (7/16) into a decimal. To convert a fraction to a decimal, we divide the numerator (the top number) by the denominator (the bottom number). So, we need to divide 7 by 16. When you perform this division, you'll find that 7 divided by 16 equals 0.4375. Now, we can combine this decimal with the whole number part of our mixed number. We simply add the whole number (2) to the decimal equivalent of the fraction (0.4375), which gives us 2 + 0.4375 = 2.4375. So, the mixed number 2 7/16 is equivalent to the decimal 2.4375. This conversion is crucial because it allows us to perform the multiplication operation easily using decimal numbers. Without this step, multiplying 2.11 by 2 7/16 directly would be much more complicated.

Performing the Multiplication

Now that we've converted our mixed number 2 7/16 into its decimal equivalent, 2.4375, we're ready to perform the multiplication. We need to multiply 2.11 by 2.4375. You can do this using a calculator or by hand using long multiplication. Let's walk through the process: First, ignore the decimal points and multiply 211 by 24375. This will give you a large number. Then, count the total number of decimal places in both original numbers. 2.11 has two decimal places, and 2.4375 has four decimal places, giving us a total of six decimal places. Finally, place the decimal point in your result so that there are six digits to the right of the decimal. When you perform the multiplication, 211 multiplied by 24375 equals 5143125. Now, we place the decimal point six places from the right, which gives us 5.143125. So, 2.11 multiplied by 2.4375 equals 5.143125. This is the unrounded result of our multiplication, but we're not quite done yet. The next crucial step is to round this number to the appropriate number of decimal places, as specified in the original problem.

Rounding to the Correct Number of Decimal Places

The final step in our calculation is rounding the result, 5.143125, to the correct number of decimal places. The question specifies that we should round to agree with the number of decimal digits in the decimal number, which is 2.11. Since 2.11 has two decimal places, we need to round our answer to two decimal places as well. To round a number to two decimal places, we look at the third decimal place. If it's 5 or greater, we round the second decimal place up. If it's less than 5, we leave the second decimal place as it is. In our result, 5.143125, the third decimal place is 3, which is less than 5. Therefore, we don't round up. We simply truncate the number after the second decimal place. So, 5.143125 rounded to two decimal places is 5.14. This means that our final answer, rounded appropriately, is 5.14. Rounding is a critical part of mathematical calculations, especially when dealing with decimals, as it ensures that our answer is presented with the appropriate level of precision. In this case, rounding to two decimal places aligns our answer with the precision of the original decimal number in the problem.

Final Answer

So, after converting the mixed number to a decimal, performing the multiplication, and rounding to the correct number of decimal places, we've arrived at our final answer. The result of 2.11 multiplied by 2 7/16, rounded to two decimal places, is 5.14. Awesome job, guys! We've successfully navigated this decimal calculation problem. Remember, the key is to break down the problem into smaller, manageable steps: convert mixed numbers to decimals, perform the multiplication, and then round the result appropriately. By following these steps, you can confidently tackle similar problems in the future. Keep practicing, and you'll become a pro at decimal calculations in no time! Remember, math can be fun, especially when we understand the process and can apply it effectively.