An element with mass 670 grams decays by 27.3% per minute. How much of the element is remaining after 9 minutes, to the nearest 10th of a gram?

Step 1: Understand the problem. The element is decaying at a rate of 27.3% per minute. This means that each minute, only 72.7% (100% - 27.3%) of the element remains.

Step 2: Convert the percentage to a decimal. 72.7% becomes 0.727.

Step 3: Apply the decay rate for each minute. After one minute, the amount of the element remaining is 670 grams * 0.727 = 487.09 grams.

Step 4: Repeat this process for the remaining 8 minutes. Each time, multiply the remaining amount by 0.727.

After 2 minutes: 487.09 grams * 0.727 = 354.38 grams. After 3 minutes: 354.38 grams * 0.727 = 257.64 grams. After 4 minutes: 257.64 grams * 0.727 = 187.36 grams. After 5 minutes: 187.36 grams * 0.727 = 136.23 grams. After 6 minutes: 136.23 grams * 0.727 = 99.07 grams. After 7 minutes: 99.07 grams * 0.727 = 72.01 grams. After 8 minutes: 72.01 grams * 0.727 = 52.34 grams. After 9 minutes: 52.34 grams * 0.727 = 38.0 grams.

Step 5: Round to the nearest tenth of a gram. The amount of the element remaining after 9 minutes is approximately 38.0 grams.