Question

A single shrimp weighs approximately 0.00027 grammes, and a shrimp company can bring over 3.1x
`{10}^(9)` shrimp in a year. How much would that many shrimp weigh? Explain in words how you would solve this in scientific notation. Make sure you explain every step in detail and why you chose to do it this way. You must keep it in scientific notation. ​

Answer 1

To calculate the total weight of 3.1 × 109 shrimp, multiply the weight of one shrimp in scientific notation (2.7 × 10-4 grammes) by the total number of shrimp, yielding a result of 8.37 × 105 grammes.

Step-by-step explanation:

To find the total weight of 3.1 × 109 shrimp, we need to multiply the weight of a single shrimp by the total number of shrimp. Given that a single shrimp weighs approximately 0.00027 grammes, we can express this weight in scientific notation as 2.7 × 10-4 grammes. To calculate the total weight, we perform the following multiplication in scientific notation:

2.7 × 10-4 grammes/shrimp × 3.1 × 109 shrimp

We multiply the coefficients (2.7 × 3.1) and add the exponents (-4 + 9) as per the rules of scientific notation, giving us:

8.37 × 105 grammes

Therefore, 3.1 × 109 shrimp would weigh 8.37 × 105 grammes. This calculation keeps the answer in scientific notation, which is compact, avoids dealing with a long string of zeros, and clearly communicates the scale of the quantity. This method is also less error-prone when working with very large or small numbers.