Rounding to required level of accuracy

[roger12]

Homework Statement

Calculate each of the following to the required level of accuracy given that each number, other than those indicated in brackets, has been obtained by measurement.

a) (3.142*1.95)/6*(3*5.44^2+1.95^2)
(power 2, divisor 6, multiplier 3)

b) (3.142*1.234)/12*( 0.424^2+0.424*0.951+0.951^2)
(power 2 and divisor 12)

Homework Equations

The Attempt at a Solution

a)My calculator gives me 94.5414368

So I think 94.5 should be the answer since 1.95 has the least number of significant figures- three. My book, though, says it is 94.54

b) The calculator gives 0.4805827337

So my answer is 0.480 because 0.424 and 0.951 each have only 3 sig figs- least number of sig figures. But my book says the answer is 0.4806


Please, show me where I am wrong.

Thanks.

 

[SammyS]

The rules for sig. fig.s are different for (addition&subtraction) than they are for (multiplication&division).

Your answer (a) looks right to me. 1.95 is a factor of all the rest, so it should limit the result to 3 sig. fig.

For (b) however, each factor in ( 0.424²+0.424*0.951+0.951²) is accurate to the 0.001 place, so the result of adding these three factors is also accurate to the 0.001 place. That give 4 sig. fig. for that result. Each of the other two factors, 3.142 & 1.234 also has 4 sig. fig.s.

 

[roger12]

The rules for sig. fig.s are different for (addition&subtraction) than they are for (multiplication&division).

Your answer (a) looks right to me. 1.95 is a factor of all the rest, so it should limit the result to 3 sig. fig.

For (b) however, each factor in ( 0.424²+0.424*0.951+0.951²) is accurate to the 0.001 place, so the result of adding these three factors is also accurate to the 0.001 place. That give 4 sig. fig. for that result. Each of the other two factors, 3.142 & 1.234 also has 4 sig. fig.s.

Thank you for the answer. I tried to apply the rule that used for (b) to another problem and got another wrong answer.

[4.62^2-(7.16-2.35)]/ [2.63+1.89* √(73.24)]

The answer is 0.8793. I thought the answer had to be rounded to 3 sig fig.

 

[SammyS]

Thank you for the answer. I tried to apply the rule that used for (b) to another problem and got another wrong answer.

[4.62^2-(7.16-2.35)]/ [2.63+1.89* √(73.24)]

The answer is 0.8793. I thought the answer had to be rounded to 3 sig fig.

Beats me!

I agree with you on this one.

Does your textbook have some unusual rules for these?

 

[SammyS]

Maybe the author treats "required level of accuracy" different than "significant figures".
?

 

[roger12]

Beats me!

I agree with you on this one.

Does your textbook have some unusual rules for these?

It's Engineering Math by Stroud. It's a great book. Sometimes unexpected problems with strange answers pop up. These are some of the few.