Solving $11 + 1 + 0.01 + 0.11 + 0.111$ A Step-by-Step Guide
Hey guys! Today, we're diving into a fun math problem that might seem a bit tricky at first glance. We've got this question: $11 + 1 + 0.01 + 0.11 + 0.111 = ? and a bunch of answer choices. It’s like a mini-puzzle, and we're going to crack it together. Don't worry if numbers aren't your best friends; we'll break it down step by step so it's super easy to follow. So, let’s put on our math hats and get started!
Understanding the Question
Before we jump into solving, let's make sure we really understand what the question is asking. We're dealing with addition here, which is a fundamental operation in math. But, we've got a mix of whole numbers and decimals, which can sometimes throw us off if we're not careful. The key is to take it slow and line things up properly. Think of it like building with LEGOs – you need to make sure each piece is connected in the right place to get the final structure correct. In this case, we need to add five different numbers together, and our goal is to find the one answer choice that matches the correct sum. So, let's get our mental math muscles warmed up and prepare to tackle this problem head-on!
Breaking Down the Numbers
Now, let's boldly break down the numbers we're working with. We have $11, which is a whole number; 1, another whole number; 0.01, a decimal; 0.11, another decimal; and 0.111, yet another decimal. Decimals can seem a bit intimidating, but they're really just parts of a whole. Think of 0.01 as one-hundredth, 0.11 as eleven-hundredths, and 0.111 as one hundred eleven-thousandths. To make things easier for ourselves, we're going to line these numbers up vertically, paying close attention to the decimal points. This is like making sure all the ingredients in a recipe are measured correctly before we mix them together. If we get the alignment right, the addition process will be a breeze. So, let's get those numbers lined up and ready to go!
Setting Up the Addition
Okay, guys, this is a crucial step! We need to set up our addition problem in a way that makes sense. Grab a piece of paper or use a digital tool – whatever works for you. Now, write down the numbers vertically, one below the other, making sure the decimal points are perfectly aligned. This is super important because it ensures we're adding the correct place values together (ones with ones, tenths with tenths, hundredths with hundredths, and so on). It's like making sure the columns in a spreadsheet line up – if they don't, the calculations will be off. If a number doesn't have a digit in a certain place value, we can add a zero as a placeholder. This helps keep things tidy and prevents mistakes. So, let's get those numbers stacked up neatly, ready for some addition action!
Performing the Addition
Alright, the moment we've been waiting for! It's time to perform the addition. Starting from the rightmost column (the thousandths place), we'll add the digits together, just like we learned in elementary school. If the sum is 10 or more, we'll carry over the tens digit to the next column, just like we're passing a baton in a relay race. We'll keep moving from right to left, adding each column and carrying over as needed. Remember to bring the decimal point straight down into our answer – it's like an anchor that keeps our decimal places in the right spot. This part might feel a bit like a workout for your brain, but don't worry, we'll take it one step at a time. Let's add those numbers up and see what we get!
Step-by-Step Calculation
Let's step-by-step calculate the answer together! First, we add the thousandths place: 0 + 0 + 0 + 0 + 1 = 1. So, we write down 1 in the thousandths place of our answer. Next, we move to the hundredths place: 0 + 0 + 1 + 1 + 1 = 3. We write down 3 in the hundredths place. Now, let's tackle the tenths place: 0 + 0 + 0 + 1 + 1 = 2. We write down 2 in the tenths place. Don't forget to bring down the decimal point! Now, for the ones place: 1 + 1 + 0 + 0 + 0 = 2. We write down 2 in the ones place. Finally, the tens place: 1 + 0 + 0 + 0 + 0 = 1. We write down 1 in the tens place. So, our sum is 12.231. Phew! That was a good mental workout. Now, let's see if our answer matches any of the choices.
Identifying the Correct Answer
Now, let's identify the correct answer from the options given. We calculated the sum to be 12.231. Now, we need to scan through the answer choices and see which one matches our result. This is like being a detective and matching the clues to the suspect. Sometimes, the answer choices might try to trick us with similar-looking numbers, so we need to be extra careful. We'll compare each digit in our calculated answer with the digits in the answer choices, making sure everything lines up perfectly. It's like checking a puzzle piece to see if it fits – if it doesn't, we move on to the next one. So, let's put on our detective hats and find the matching answer!
Matching the Result
Alright, let's match the result! We found that the sum of is 12.231. Now, let's look at the answer choices: A. 12.231, B. 12.222, C. 13.23, D. 15.21. Bingo! Option A, 12.231, perfectly matches our calculated answer. It's like finding the missing piece of a jigsaw puzzle – everything clicks into place. The other options are close, but they have slight differences in the decimal places, which makes them incorrect. So, we've successfully identified the right answer! Give yourselves a pat on the back, mathletes!
Conclusion
Great job, everyone! We've successfully navigated this math problem and found the correct answer. We started by understanding the question, then broke down the numbers, set up the addition, performed the calculation step-by-step, and finally, identified the matching answer choice. This whole process is like following a roadmap to reach a destination – each step is important, and if we follow them carefully, we'll arrive at the right place. Remember, math isn't about memorizing formulas; it's about understanding the process and applying it logically. So, keep practicing, keep exploring, and most importantly, keep having fun with math! You guys are awesome!