We are currently studying significant digits/figures. I was asked to add 150 ml with 76.9 ml, plus 209 ml plus 0.036 ml. The book says the answer is 440, but I got 435. (the complete answer, without applying the significant digits rule is 435.936) How did I do this incorrectly?
The units digit is not significant (the zero in 150)
150+80+210=440
To determine how you might have calculated the answer incorrectly, we need to consider the rules for significant figures in addition.
In general, when adding or subtracting numbers, you should consider the least precise measurement and limit your answer to the same number of decimal places as the least precise measurement. In this case, the least precise measurement is 0.036 ml.
Let's break down the calculations step by step:
1. Adding 150 ml and 76.9 ml:
- Since both numbers have zero digits after the decimal point, the sum should also have zero digits after the decimal point. Therefore, the answer should be 227 ml (not changing the decimal portion).
2. Next, adding 227 ml and 209 ml:
- Following the same rule, since none of the numbers have any digits after the decimal point, the sum should have zero digits after the decimal point. So, the answer should be 436 ml (again, not changing the decimal portion).
3. Finally, adding 436 ml and 0.036 ml:
- This time, we need to consider the least precise measurement, which is 0.036 ml with three digits after the decimal point. Thus, the sum should have three digits after the decimal point.
- Adding the numbers, we get 436.036 ml.
Now, let's round the answer to the correct number of significant figures. In this case, we have three significant figures from "436" and three decimal places from "0.036".
- By applying the rule of rounding, the answer becomes 436 ml (since the next digit after the third decimal place, "6", is less than 5, and thus, we round down).
Therefore, the correct answer, while considering significant figures, is 436 ml, not 435 ml. The answer provided in the book as 440 ml seems to deviate from the rules of significant figures.