Solving 3×10^8/1.5 A Step-by-Step Guide

Hey guys! Ever stumbled upon a mathematical expression that looks a bit intimidating at first glance? Well, today we're going to break down a seemingly complex problem into simple, digestible steps. We'll be tackling the expression 3×10^8/1.5, which might look like a jumble of numbers and symbols, but trust me, it’s quite manageable once we understand the underlying concepts. This isn't just about getting the right answer; it's about understanding the process and building a strong foundation in mathematical problem-solving. So, let's dive in and unravel this numerical puzzle together! We will go through each step in detail, ensuring that you not only understand how to solve this particular problem but also grasp the general principles that can be applied to similar calculations.

Decoding the Expression: What Does It All Mean?

Before we start crunching numbers, let's break down what the expression 3×10^8/1.5 actually means. The heart of this expression lies in understanding scientific notation and the order of operations. Scientific notation, in this case, 10^8, is a way of expressing very large or very small numbers in a compact and convenient form. It’s essentially a number multiplied by a power of 10. Here, 10^8 means 10 raised to the power of 8, which is 1 followed by 8 zeros – that's 100,000,000 (one hundred million)! So, 3×10^8 is simply 3 multiplied by 100,000,000, resulting in 300,000,000 (three hundred million). This is a massive number, and scientific notation helps us handle it without writing out all those zeros. Now, the division part: /1.5 means we're dividing the result of 3×10^8 by 1.5. Division is one of the fundamental arithmetic operations, and in this context, it helps us scale down the large number we obtained earlier. Remember, the order of operations (often remembered by the acronym PEMDAS/BODMAS) dictates that we perform multiplication and division from left to right before addition and subtraction. In our expression, we have multiplication and division, so we perform them in the order they appear. This understanding is crucial because changing the order would lead to a completely different and incorrect answer. So, with a clear understanding of each component, we're ready to move on to the next step: actually performing the calculation. This foundational knowledge is key to tackling not just this problem, but a wide range of mathematical challenges. So, let's keep this in mind as we proceed!

Step-by-Step Calculation: Solving 3×10^8/1.5

Alright, let's get our hands dirty and walk through the calculation of 3×10^8/1.5 step by step. This isn't just about getting the final answer; it's about understanding the process so you can tackle similar problems with confidence. First, we'll address the multiplication part: 3×10^8. As we discussed earlier, 10^8 is 100,000,000. So, 3×10^8 is simply 3 multiplied by 100,000,000, which equals 300,000,000. That's a big number! Writing it out like this can be a bit cumbersome, but it helps to visualize the magnitude we're dealing with. Now comes the division part: We need to divide 300,000,000 by 1.5. This might seem daunting, but we can simplify it. Dividing by 1.5 is the same as dividing by 3/2 (since 1.5 is equal to 3 divided by 2). Remember the rule for dividing by a fraction? You flip the fraction and multiply! So, dividing by 3/2 is the same as multiplying by 2/3. This makes our calculation much easier. So, we now have 300,000,000 multiplied by 2/3. We can think of this as (300,000,000 * 2) / 3. First, 300,000,000 multiplied by 2 gives us 600,000,000. Then, we divide 600,000,000 by 3. This is a straightforward division, and it gives us 200,000,000. So, the final answer to 3×10^8/1.5 is 200,000,000. See? It wasn't as scary as it looked! By breaking the problem down into smaller, manageable steps, we were able to arrive at the solution with ease. This step-by-step approach is a powerful tool in mathematics, and it can help you conquer even the most complex problems. Now that we've cracked the calculation, let's think about why this kind of problem might be relevant in the real world.

Real-World Applications: Where Does This Math Come In?

Okay, now that we've successfully solved 3×10^8/1.5, you might be wondering,