1. A skyscraper has a mass of 2.2 x 10^5 tons. Another skyscraper in the same town has a mass of 3.7 x 10^5 tons. What is the combined mass, in tons, of the two skyscrapers? Use scientific notation to express your answer to 1 decimal place.

Question

An abstract aerial view of a city skyline, showing two expansive skyscrapers of differing heights. Beside them, two insect-like figures of differing sizes symbolize the tiny creatures in the question. In the foreground, a detailed illustration of an American football field and one from Canada, each with distinct features and dimensions. In another section of the image, a magnified human hair and a fingernail with detailed measurements to indicate their sizes.

1. A skyscraper has a mass of 2.2 x 10^5 tons. Another skyscraper in the same town has a mass of 3.7 x 10^5 tons. What is the combined mass, in tons, of the two skyscrapers? Use scientific notation to express your answer to 1 decimal place.

2. A certain insect is approximately 4 x 10^-2 inches long. A second insect is about 1.3 x 10^-1 inches long. What is the total length of the two insects in inches? Use scientific notation to express your answer to 1 decimal place.
3. What is the sum of 6.3 x 10^3 and 2.41 x 10^4? Use scientific notation to express your answer.
4. An American football field has an area of 6.4 x 10^3 square yards. A Canadian football field is 3,350 square yards larger. What is the area of a Canadian football field? Write your answer in scientific notation to 2 decimal places. __ x 10^3 square yards.
5. A human hair has a diameter of about 4 x 10^-3 inches. A fingernail is about 0.011 inches thicker. How thick is a fingernail? Write your answer as a decimal to 3 places. ___ Inches

Answer 1

1. The combined mass of the two skyscrapers is (2.2 x 10^5 + 3.7 x 10^5) tons = 5.9 x 10^5 tons.

2. The total length of the two insects is (4 x 10^-2 + 1.3 x 10^-1) inches = 1.7 x 10^-1 inches.
3. The sum of 6.3 x 10^3 and 2.41 x 10^4 is 2.41 x 10^4 + 6.3 x 10^3 = 2.71 x 10^4.
4. The area of a Canadian football field is (6.4 x 10^3 + 3,350) square yards = 9.75 x 10^3 square yards.
5. A fingernail is 0.011 inches thicker than a human hair, so the thickness of a fingernail is 4 x 10^-3 + 0.011 inches ≈ 0.014 inches.

Answer 2

3 is wrong

Answer 3

Apologies for the error. Let's correct the answer for question 3:

3. The sum of 6.3 x 10^3 and 2.41 x 10^4 is (6.3 x 10^3 + 2.41 x 10^4) = 2.77 x 10^4.

Answer 4

Apologies for the mistake again. Let's correct the answer for question 3:

3. The sum of 6.3 x 10^3 and 2.41 x 10^4 is (6.3 x 10^3 + 2.41 x 10^4) = 2.04 x 10^4.

Answer 5

5 is wrong

Answer 6

Apologies for the mistake. Let's correct the answer for question 5:

5. A fingernail is 0.011 inches thicker than a human hair, so the thickness of a fingernail is (4 x 10^-3 + 0.011) inches = 0.015 inches.