1. Is it more appropriate to use scientific notation for approximates or exact numbers? why?

2. In one plantation, there are 2700 young trees correct to 2 significant figures. In the other there are 830 full grown trees, correct to 2 significant figures.

a) Why is it incorrect to say the company has a total of 3530 trees in two plantations, correct to 2 significant figures?

b) On the figures given, what is the least number of trees they could have in the two plantations?

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1. Scientific notation is more appropriate for expressing very large or very small numbers, especially when dealing with approximations. This is because scientific notation allows us to easily represent and comprehend the magnitude of a number by expressing it as a coefficient multiplied by a power of 10. For example, the number 100,000,000 can be written as 1 x 10^8 in scientific notation, which clearly conveys the magnitude of the number.

On the other hand, exact numbers, such as whole numbers or integers, are typically best represented in standard decimal notation. Scientific notation is not needed for exact numbers because there is no need to approximate or express them in a compact form.

2.
a) It is incorrect to say the company has a total of 3530 trees in two plantations, correct to 2 significant figures because the significant figures in each individual count are limited to 2. When combining or adding numbers with different levels of precision, the result should also be reported with the same level of precision.

In this case, the counts are rounded to 2 significant figures, so the total count should also be rounded to 2 significant figures. The correct way to express the total would be "3500 trees" or "3.5 x 10^3 trees" if expressed in scientific notation.

b) To find the least number of trees they could have in the two plantations, we must consider the lower limit of each count.

For the young trees with 2700 trees, correct to 2 significant figures, the lower limit is obtained by considering the first doubtful digit, which is the third digit. Since the third digit is 0, the most conservative estimate is to assume that the actual count can be as low as 2600.

For the full-grown trees with 830 trees, correct to 2 significant figures, the lower limit is also obtained by considering the first doubtful digit, which is the third digit. Since the third digit is 0, the most conservative estimate is to assume that the actual count can be as low as 820.

To find the least number of trees they could have in the two plantations, we simply add these lower limits together: 2600 + 820 = 3420 trees. Therefore, the least number of trees they could have in the two plantations is 3420 trees.