I\'m confused in significant figures and calculations. I know for multiplication

Question

I'm confused in significant figures and calculations. I know for multiplication or division, the number of the sig figsis same as the number in the least precise measurement used in calculation and for addition or subtraction, the result has the same number of decimal places as the least precise measurement used in the calculation. I am suffering from the calculation which both have multiplication or division and addition or subtraction. For example, when we diverse celcius temperature 39.2 to fahrenheit, we use 39.2*9/5+32 and the answer is 102.56 and when we round the ansxer sheet said it is 102.6. (9/5 and 32 are exact numbers) But another example to change 801 celcius to fahreneit, it is 1473.8 and when we round, the answer sheet says it is 1470. I thought that when calculations are mixed, we use the least precise number's decimal places to round the answer, but when I see the second example, I think the number of sig figs in he least precise number is used to find the answer. I can't find the commom rule. In summury, I want to know how to calculate and round numbers when the signs are mixed.    Help me please.

Explanation / Answer

Use the relation

where C denotes the temperature in the Celsius scale and F is the temperature in the Fahrenheit scale.

For the first example, we have C = 39.2; plug in values and obtain

The least precise measurement has one sig. fig and hence, we round off the result to one sign. fig. and the answer is 102.6 F (ans).

In the next example, we have C = 801; plug in values and obtain

The answer you obtained is correct. 1470 and 1473.8 are different numbers (there is a difference of 3.8 F) and this difference cannot be due to rounding off of numbers. At best, the result could be 1474 F, but if 801 is the temperature in Celsius scale, there is no way that you are getting 1470. However, only if the temperature is 799°C, you will get 1470 F as the answer. This seems like a calculation error rather than rounding off error.

Moreover, the rules you stated are the ones we should adhere to; there are no other hidden rules.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.