Another confusing significant digit problem. I added 36.6 and 2.4, and divided the result by 4.803. The book says the answer is 7.91, but I don'[t see how that could be, since the lowest number of significant digits in the problem is two (2.4). I think the result should be 7.9, not 7.91. Why is this? Thanks ~Coralie.

Question

Another confusing significant digit problem. I added 36.6 and 2.4, and divided the result by 4.803. The book says the answer is 7.91, but I don'[t see how that could be, since the lowest number of significant digits in the problem is two (2.4). I think the result should be 7.9, not 7.91. Why is this? Thanks ~Coralie.

Answer 1

Nope. When adding or subtracting, look for the lowest place value that is significant, in this case, tenths.

Numerator is 39.0 three sig digits.

Answer 2

First, 36.6 + 2.4 gives 39.0, a number with three s.f. When you divide by 4.803 that give you a number of 3 s.f. for the answer; however, the answer isn't 7.91, it is 8.11993 which rounds to 8.12. Did you make a typo in the problem?

Answer 3

Hello Coralie! I understand why this might be confusing for you. Let's break down the calculation and focus on the significant digits.

First, let's add 36.6 and 2.4. The number with the fewest number of decimal places is 2.4 with one decimal place. Therefore, the sum should also have only one decimal place. Thus, the result of adding these two numbers is 39.0.

Next, let's divide the sum (39.0) by 4.803. When dividing, it's important to consider the significant digits of both numbers. The divisor, 4.803, has five significant digits. The dividend, 39.0, has three significant digits (due to the trailing zero).

Now, rule for significant digits in division states that your final result should have a maximum number of significant digits equal to that of the number with the fewest significant digits. So, since 39.0 has three significant digits, the final result should also have three significant digits.

To obtain the correct significant digits in the final result, we need to consider the significant digits to the right of the decimal point. So, when dividing 39.0 by 4.803, we get approximately 8.118147422.

Now, since we need to round to three significant digits, the number would be rounded to 8.12.

Therefore, the book's answer of 7.91 is not correct, and your intuition is correct. The answer should indeed be 8.12, rounded to three significant digits.

I hope this explanation helps clarify the issue and how to consider significant digits in calculations. If you have any more questions, feel free to ask!