Calculate 3.03 Times 21.3 Round To The Nearest Hundredth

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In this article, we will delve into the process of calculating the product of two decimal numbers, 3.03 and 21.3, and rounding the result to the nearest hundredth. This is a fundamental mathematical operation with practical applications in various fields, from finance and engineering to everyday calculations. Understanding how to perform this calculation accurately is crucial for problem-solving and decision-making.

Decimal multiplication might seem daunting at first, but by breaking it down into simpler steps, we can easily arrive at the correct answer. We'll start by multiplying the numbers as if they were whole numbers, and then we'll take into account the decimal places to position the decimal point correctly in the final product. Rounding to the nearest hundredth involves looking at the digit in the thousandths place and determining whether to round up or down. This ensures that our answer is accurate to two decimal places.

Before we dive into the specific calculation, let's review the basics of decimal multiplication. When multiplying decimals, the first step is to ignore the decimal points and treat the numbers as whole numbers. Multiply them as you normally would, and then count the total number of decimal places in the original numbers. This total will determine where you place the decimal point in the final product.

For example, if you are multiplying 3.03 (two decimal places) by 21.3 (one decimal place), you would first multiply 303 by 213, which gives you 64539. Then, since there are a total of three decimal places (two in 3.03 and one in 21.3), you would place the decimal point three places from the right in the product, resulting in 64.539. This preliminary result is crucial, and the next step involves rounding it to the nearest hundredth to get the final answer.

Let's walk through the step-by-step calculation of multiplying 3.03 and 21.3.

  1. Ignore the decimal points: Treat 3.03 as 303 and 21.3 as 213.
  2. Multiply the whole numbers:
      303
x 213
------
  909  (303 x 3)
303   (303 x 1, shifted one position to the left)

606 (303 x 2, shifted two positions to the left) ------ 64539 ``` 3. Count the decimal places: 3.03 has two decimal places, and 21.3 has one decimal place, totaling three decimal places. 4. Place the decimal point: In the product 64539, count three places from the right and insert the decimal point: 64.539.

This gives us a preliminary product of 64.539. Now, we need to round this number to the nearest hundredth. Rounding decimals is a critical skill in mathematics, ensuring precision and relevance in many practical applications.

Rounding to the nearest hundredth means we want to keep two decimal places. To do this, we look at the digit in the thousandths place (the third decimal place). If this digit is 5 or greater, we round up the hundredths digit. If it is 4 or less, we leave the hundredths digit as it is.

In our case, the product is 64.539. The digit in the thousandths place is 9, which is greater than 5. Therefore, we round up the hundredths digit (3) by one.

So, 64.539 rounded to the nearest hundredth is 64.54. This ensures that our final answer is accurate and meets the required precision. Accurate rounding is essential in various fields, such as finance and engineering, where even small discrepancies can have significant consequences.

Therefore, the product of 3.03 and 21.3, rounded to the nearest hundredth, is 64.54.

The ability to accurately multiply decimals and round the results is crucial in various real-world scenarios. Let's explore a few practical applications:

  1. Finance: Calculating interest on loans or investments often involves multiplying decimal numbers and rounding to the nearest cent (hundredth of a dollar). For instance, if you have a loan of $3030 at an annual interest rate of 2.13%, calculating the annual interest involves multiplying these numbers. The final result, rounded to the nearest cent, gives you the precise interest amount.

  2. Retail: Determining the total cost of multiple items with decimal prices requires multiplying the price per item by the quantity purchased. For example, if an item costs $3.03 and a customer buys 21.3 units (perhaps measured in weight, like kilograms), the total cost is calculated by multiplying these values. The rounded result represents the actual amount the customer needs to pay.

  3. Engineering: In engineering calculations, precise measurements and calculations are vital. Multiplying decimal values might be necessary for calculating dimensions, volumes, or material costs. Rounding to the nearest hundredth can provide a balance between accuracy and practicality, ensuring that the calculations are precise enough for the task at hand without being overly complex.

  4. Cooking and Baking: Recipes often require scaling ingredients up or down, which may involve multiplying decimal quantities. For instance, if a recipe calls for 3.03 ounces of an ingredient and you want to increase the recipe by a factor of 21.3, you need to perform this multiplication. Accurate rounding ensures that the proportions of ingredients remain consistent, resulting in a successful dish.

  5. Science: Scientific experiments frequently involve measurements with decimal values. Calculating concentrations, volumes, or other scientific quantities may require decimal multiplication. Rounding the results appropriately helps in presenting data clearly and accurately in scientific reports and analyses.

In each of these scenarios, the ability to perform decimal multiplication and round the result to the nearest hundredth is invaluable. Mastering this skill ensures accuracy and precision in various practical contexts.

While the process of multiplying decimals and rounding is straightforward, there are common mistakes that individuals often make. Being aware of these pitfalls can help you avoid errors and ensure accuracy in your calculations.

  1. Misplacing the decimal point: One of the most frequent errors is incorrectly placing the decimal point in the final product. This usually occurs when the total number of decimal places is miscalculated, or the decimal point is counted from the wrong end. To avoid this, always double-check the number of decimal places in the original numbers and count from the right in the product.

  2. Forgetting to round: Another common mistake is failing to round the result to the specified decimal place. If the question asks for the answer to the nearest hundredth, it is essential to round the final product accordingly. Overlooking this step can lead to an inaccurate answer.

  3. Rounding prematurely: Rounding intermediate calculations can introduce errors in the final result. It is best practice to perform all calculations with as many decimal places as possible and only round the final answer. This ensures that the cumulative effect of rounding errors is minimized.

  4. Incorrectly applying rounding rules: The rules for rounding are specific: if the digit to the right of the desired decimal place is 5 or greater, round up; if it is 4 or less, round down. Misapplying these rules can lead to incorrect rounding. Always remember to look at the digit immediately to the right of the place you are rounding to.

  5. Calculator errors: While calculators are helpful tools, relying solely on them without understanding the underlying principles can be problematic. It is essential to understand the process and check the calculator's result for reasonableness. Sometimes, entering numbers incorrectly or misinterpreting the display can lead to errors.

By being mindful of these common mistakes and taking the necessary precautions, you can significantly improve your accuracy in decimal multiplication and rounding.

To reinforce your understanding and skills in multiplying decimals and rounding, let's work through a few practice problems:

  1. Calculate the product of 4.25 and 15.8 and round the result to the nearest hundredth.

    • Multiply 425 by 158: 425 * 158 = 67150
    • Total decimal places: 2 (in 4.25) + 1 (in 15.8) = 3
    • Place the decimal point: 67.150
    • Round to the nearest hundredth: 67.15 (since the thousandths digit is 0)

  2. Find the product of 12.75 and 2.345, rounded to the nearest hundredth.

    • Multiply 1275 by 2345: 1275 * 2345 = 2990375
    • Total decimal places: 2 (in 12.75) + 3 (in 2.345) = 5
    • Place the decimal point: 29.90375
    • Round to the nearest hundredth: 29.90 (since the thousandths digit is 3)

  3. What is the product of 0.875 and 9.6, rounded to the nearest hundredth?

    • Multiply 875 by 96: 875 * 96 = 84000
    • Total decimal places: 3 (in 0.875) + 1 (in 9.6) = 4
    • Place the decimal point: 8.4000
    • Round to the nearest hundredth: 8.40 (since the thousandths digit is 0)

  4. Calculate 19.5 multiplied by 6.25 and round to the nearest hundredth.

    • Multiply 195 by 625: 195 * 625 = 121875
    • Total decimal places: 1 (in 19.5) + 2 (in 6.25) = 3
    • Place the decimal point: 121.875
    • Round to the nearest hundredth: 121.88 (since the thousandths digit is 5)

By working through these examples, you can build confidence in your ability to multiply decimals and round accurately.

In summary, calculating the product of 3.03 and 21.3 and rounding to the nearest hundredth involves several key steps: multiplying the numbers as whole numbers, counting the total decimal places, placing the decimal point in the product, and applying the rounding rules. The final result, as we've determined, is 64.54.

This skill is not just a mathematical exercise; it has practical applications in numerous real-life scenarios, including finance, retail, engineering, cooking, and science. Mastering this skill ensures accuracy and precision in various calculations, which is essential for problem-solving and decision-making.

By understanding the underlying principles and practicing regularly, you can enhance your mathematical proficiency and confidently tackle similar problems in the future. Remember to avoid common mistakes, such as misplacing the decimal point or rounding prematurely, to ensure accurate results.