Significant Figures In 1.22 X 0.91? Explained!

When we're diving into calculations in chemistry, it's super important to understand significant figures. They're like the VIPs of our numbers, telling us how precise our measurements and calculations really are. So, let's break down this problem step by step, making sure we nail not only the answer but also the why behind it.

Understanding Significant Figures

First things first, what exactly are significant figures? Guys, they're the digits in a number that carry meaningful information about its precision. Non-zero digits are always significant – easy peasy! But things get a bit trickier with zeros. Here’s a quick rundown:

• Non-zero digits: Always significant (1, 2, 3, …, 9)
• Zeros between non-zero digits: Significant (e.g., 102 has three significant figures)
• Leading zeros: Never significant (e.g., 0.001 has one significant figure)
• Trailing zeros in a number containing a decimal point: Always significant (e.g., 1.20 has three significant figures)
• Trailing zeros in a number not containing a decimal point: Not significant (e.g., 100 may have one, two, or three significant figures – tricky, right?)

Why do we even care about significant figures? Imagine you're mixing chemicals for an experiment. If you measure out a quantity with low precision and use that in a calculation, your final result can't be more precise than your least precise measurement. Significant figures help us keep our calculations honest and reflect the true accuracy of our results.

When multiplying or dividing, the number of significant figures in the final answer should match the number with the fewest significant figures in the calculation. Remember this rule – it's our golden ticket for this problem!

Solving the Problem: $1.22 \times 0.91$

Okay, let’s tackle our problem: $1.22 \times 0.91$. We need to figure out how many significant figures will be in the final answer. To do this, we'll first identify the number of significant figures in each number.

Step 1: Identify Significant Figures in Each Number

• 1.22: This number has three non-zero digits, so it has three significant figures. No sweat here!
• 0.91: This number has two non-zero digits (9 and 1). The zero before the decimal point doesn't count (it's a leading zero). So, 0.91 has two significant figures.

Step 2: Apply the Multiplication Rule

Remember our golden rule? When multiplying, the final answer can only have as many significant figures as the number with the fewest significant figures. In this case, 0.91 has the fewest – just two significant figures.

So, when we multiply $1.22 \times 0.91$, the answer should be rounded to two significant figures.

Step 3: Calculate and Round

Let's go ahead and do the calculation:

$1.22 \times 0.91 = 1.1102$

Now, we need to round this to two significant figures. The first two digits are 1 and 1. The next digit is 1, which is less than 5, so we round down.

Therefore, the final answer, rounded to two significant figures, is 1.1.

Discussion: The Importance of Precision

Guys, precision in scientific calculations isn't just about getting the right number; it’s about accurately representing the certainty (or uncertainty) in our measurements. Using the correct number of significant figures prevents us from overstating the accuracy of our results. It's a way of being scientifically honest! In practical terms, imagine you’re titrating an acid with a base in a lab. If you read the volume of the titrant to four decimal places when your burette only measures to two, you're essentially claiming a level of precision you don’t actually have. This could lead to inaccurate results and flawed conclusions. Therefore, understanding and applying the rules for significant figures are crucial for reliable and reproducible scientific work. This ensures that your calculations reflect the reality of your measurements, not an idealized version of them. Always consider the tools you are using and their limitations. If you're using a balance that measures to the nearest tenth of a gram, your final results can't be accurate to the nearest hundredth of a gram. Respect the limitations of your equipment and report your results accordingly.

Conclusion

So, if you calculated $1.22 \times 0.91$, the answer would have two significant figures. We figured this out by identifying the number of significant figures in each original number and applying the rule that the final answer should have the same number of significant figures as the number with the fewest. It's all about precision and scientific honesty, my friends!

Therefore, the correct answer to the question