I am supposed to add up these numbers, using the significant digits rules.
150
76.9
209
.036
I got 435.936. Following the sig. digs. rules, it would be 435.9, right? How does this then equal 440 as my science books says? Thank you so much.
The lowest sig fig in all the number you added was 2. So you should round your total which is 435.936 so you can get 2 sig figs in your answer. 440 has 2 sig figs.
Chopsticks is almost right. The least sig digit is the tens (150) so nothing past that makes any sense.
440
To determine the correct number of significant digits in the final answer when doing addition or subtraction, you need to consider the number with the least number of decimal places.
Let's look at the numbers you provided:
150 (3 significant digits)
76.9 (3 significant digits)
209 (3 significant digits)
0.036 (2 significant digits)
If we add these numbers without considering significant digits, we get 435.936. However, when applying the significant digits rules, we need to round the answer according to the number with the least number of decimal places, which in this case is 0.036 with 2 significant digits.
So when we round our result to 2 significant digits, we get 440 (instead of 435.9 as you mentioned). Since the number 0.036 has only 2 significant digits, we round our final answer to match that precision.
Your science book is correct in stating that the answer is 440, as it aligns with the rules for significant digits.