significant numbers

2.8723 * 1.6 = 4.59568. Is it 4.6 because it is the smallest number you are multiplying it by in the sum? e.g. 2.8723 has 5 signifigant figures but 1.6 has 2 so the answer has no more than 2.Smallest number of significant figures.
With addition is it the smallest number afte the decimal point e.g. 3.968 + 2.02 + 4.7832 = 8.0374 = 0.05 because it is the smallest number of decimal places in the sum is 1. e.g. 2.02 = 1 significant figure after decimal point?

Significant figures are a way to represent the precision of a number. They indicate the meaningful digits in a number, taking into account both the digits before and after the decimal point.

In multiplication or division, the rule is generally to round the final answer to the same number of significant figures as the number with the fewest significant figures. This is because the result of the calculation cannot be more precise than the least precise number involved.

In your example, 2.8723 has 5 significant figures, and 1.6 has 2 significant figures. To determine the number of significant figures in the product, you take the number with the fewest significant figures, which is 1.6, and round the product to the same number of significant figures. Therefore, the answer, 4.59568, would be rounded to 4.6 because 1.6 dictates the maximum number of significant figures.

In addition or subtraction, you typically round the result to the same decimal place as the number with the least number of decimal places. This is because the precision of the result cannot exceed the least precise number involved.

In your second example, 3.968 has 3 decimal places, 2.02 has 2 decimal places, and 4.7832 has 4 decimal places. To determine the number of decimal places in the sum, you look at the number with the fewest decimal places, which is 2.02. Therefore, the answer, 8.0374, would be rounded to 8.04, not 0.05.

It's important to note that these rules for determining significant figures are just guidelines and may vary depending on the context and specific calculations being performed.