Question

Carry out the following operations as if they were calculations of experimental results, and express each answer in the correct units with the correct number of significant figures: (a) 5.6792 m + 0.6 m + 4.33 m (b) 3.70 g - 2.9133 g (c) 4.51 cm x 3.6666 cm

Answer 1

The significant figures in the answers of the additions, subtractions, and multiplications must match the precision of the least precise measurement used in the calculations. For the provided problems: (a) the result is 10.61 m, (b) the result is 0.79 g, and (c) the result is 16.5 cm^2.

Step-by-step explanation:

When carrying out operations and calculation of experimental results, the significant figures in the answer must reflect the precision of the least precise measurement used in the calculations.

(a) When you add measurements together (5.6792 m + 0.6 m + 4.33 m), the result should be rounded off to the least number of decimal places of the measurement with the least number of decimal places. Here, 0.6 m has no decimal places, so the result will be rounded to the nearest whole number: 10.61 m.

(b) When subtracting (3.70 g - 2.9133 g), the answer should have the same number of decimal places as the measurement with the least number of decimal places. The answer, rounded to two decimal places, is: 0.79 g.

(c) For multiplication (4.51 cm x 3.6666 cm), you round the answer to the same number of significant figures as the measurement with the fewest significant figures. Since 4.51 cm has three significant figures, the result will be rounded to three significant figures: 16.5 cm2.

Answer 2

Step-by-step explanation:

1. 5.6792 m + 0.6 m + 4.33 m

Adding gives: 10.6092 m

Of the three measurements given, the one with the least number of decimal places has to be considered since we are adding the measurements. 0.6 m has only one decimal place. So the answer has to be rounded off to one decimal place.

Hence the answer = 10.6 m

2. 3.70 g - 2.9133 g

Subtracting gives: 0.7867

The answer has to be rounded off to the least number of decimal places which is 2 , (3.70)

Hence the answer = 0.79 g

3. 4.51 cm * 3.6666 cm

Multiplying gives: 16.536366

For multiplication, the answer needs to be rounded off to the least number of significant figures in the given measurements. 4.51 cm has three significant figures.

So rounding off, the answer = 16.5 cm²