The approximate weights of two animals are 5.12 x 102 lbs. and 6.8 x 102 lbs. Find the total weight of the two animals. Write the final answer in scientific notation with the correct number of significant digits.
a) 1.2 x 103 lbs.
b) 1.19 x 103 lbs.
c) 11 x 102 lbs.
d) 5.8 x 102 lbs.
To find the total weight of the two animals, we simply add their weights together.
(5.12 x 10^2 lbs.) + (6.8 x 10^2 lbs.) = 1.792 x 10^2 lbs.
Therefore, the correct answer is d) 5.8 x 10^2 lbs.
To find the total weight of the two animals, we need to add their weights together.
Starting with the approximate weight of the first animal, which is 5.12 x 102 lbs, and the approximate weight of the second animal, which is 6.8 x 102 lbs, we can add them:
5.12 x 102 lbs + 6.8 x 102 lbs
Since both weights are in scientific notation and have the same exponent (102), we can simply add the coefficients:
5.12 + 6.8 = 11.92
Now, we need to convert this result to scientific notation. To do this, we will move the decimal point one place to the left and adjust the exponent accordingly:
11.92 x 102 lbs = 1.192 x 103 lbs
Therefore, the total weight of the two animals is approximately 1.192 x 103 lbs.
The final answer with the correct number of significant digits is option b) 1.19 x 103 lbs.
To find the total weight of the two animals, you need to add their weights together.
The first animal weighs 5.12 x 102 lbs., and the second animal weighs 6.8 x 102 lbs.
To add these numbers together, you align the decimal points and add the two values:
5.12 x 102
+ 6.8 x 102
-------------
11.92 x 102
The sum of the weights is 11.92 x 102 lbs.
However, when you express this value in scientific notation, there should only be one digit to the left of the decimal point. So, we need to adjust the decimal point to the right.
Since 11.92 x 102 means moving the decimal point two places to the right, we need to shift it once to get a single digit to the left of the decimal point:
11.92 x 102
= 1.192 x 103
So, the total weight of the two animals, expressed in scientific notation with the correct number of significant digits, is 1.192 x 103 lbs.
Therefore, the correct answer is option b) 1.19 x 103 lbs.