COLLEGE PHYSICS-CONNECT ACCESS
COLLEGE PHYSICS-CONNECT ACCESS
5th Edition
ISBN: 9781260486834
Author: GIAMBATTISTA
Publisher: MCG
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Question
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Chapter 1, Problem 68P

(a)

To determine

The calculation of 186.300+0.0030.

(a)

Expert Solution
Check Mark

Answer to Problem 68P

The calculation of 186.300+0.0030 is 186.303.

Explanation of Solution

Calculate the given operation

    186.300+0.0030=186.3030=186.303

Conclusion:

Therefore, the calculation of 186.300+0.0030 is 186.303.

(b)

To determine

The calculation of 186.300-0.0030.

(b)

Expert Solution
Check Mark

Answer to Problem 68P

The calculation of 186.300-0.0030 is 186.297.

Explanation of Solution

Calculate the given operation

    186.3000.0030=186.2970=186.297

Conclusion:

Therefore, the calculation of 186.300+0.0030 is 186.297.

(c)

To determine

The calculation of 186.300×0.0030.

(c)

Expert Solution
Check Mark

Answer to Problem 68P

The calculation of 186.300×0.0030 is 0.5589.

Explanation of Solution

Calculate the given operation

    186.300×0.0030=0.5589

Conclusion:

Therefore, the calculation of 186.300+0.0030 is 0.5589.

(d)

To determine

The calculation of 186.300/0.0030.

(d)

Expert Solution
Check Mark

Answer to Problem 68P

The calculation of 186.300/0.0030 is 62100.

Explanation of Solution

Calculate the given operation

    186.300/0.0030=62100

Conclusion:

Therefore, the calculation of 186.300+0.0030 is 62100.

(e)

To determine

The percentage error in part (a) and (b) if 0.0030 is ignored.

(e)

Expert Solution
Check Mark

Answer to Problem 68P

The percentage error in part(a) and (b) is 1.61×103% which is very small and can be neglected whereas in part (c) and (d) the percentage error is too large to be neglected.

Explanation of Solution

Write the formula for percentage error

    %error=|xappxcorxcor|×100        (I)

Here, xapp is the approximate value and xcor is the exact value.

Conclusion:

(a) Substitute 186.3030 for xcor and 186.300 for xapp in equation (I) to find error

    %error=|186.300186.3030186.3030|×100=1.61×103%

 (b) Substitute 186.297 for xcor and 186.300 for xapp in equation (I) to find error

    %error=|186.300186.297186.297|×100=1.61×103%

(c) Substitute 0.5589 for xcor and 186.300 for xapp in equation (I) to find error

    %error=|186.3000.55890.5589|×100=3.3233×104%

(d) Substitute 62100 for xcor and 186.300 for xapp in equation (I) to find error

    %error=|186.3006210062100|×100=99.7%

Therefore, the percentage error in part(a) and (b) is 1.61×103% which is very small and can be neglected whereas in part (c) and (d) the percentage error is too large to be neglected.

(f)

To determine

The rule to be followed while ignoring smaller numbers.

(f)

Expert Solution
Check Mark

Answer to Problem 68P

Smaller numbers can be ignored during subtraction and multiplication whereas it can’t be neglected during multiplication and division.

Explanation of Solution

Adding or subtracting a smaller number doesn’t make much of a difference to the calculation as they result in a smaller percentage error. Hence they can be neglected.

While multiplying and dividing, smaller numbers need to be taken into account as they make a significant difference in the answer. Their percentage error is too large to be neglected.

Conclusion:

(a) Substitute 186.3030 for xcor and 186.300 for xapp in equation (I) to find error

    %error=|186.300186.3030186.3030|×100=1.61×103%

(a) Substitute 186.297 for xcor and 186.300 for xapp in equation (I) to find error

    %error=|186.300186.297186.297|×100=1.61×103%

Therefore, smaller numbers can be ignored during subtraction and multiplication whereas it can’t be neglected during multiplication and division.

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Chapter 1 Solutions

COLLEGE PHYSICS-CONNECT ACCESS

Ch. 1.6 - Prob. 1.8PPCh. 1.6 - Prob. 1.9PPCh. 1.6 - Prob. 1.6CPCh. 1.8 - Prob. 1.10PPCh. 1.9 - Prob. 1.11PPCh. 1.9 - What value of k would you calculate by using only...Ch. 1 - Prob. 1CQCh. 1 - Why must words be carefully defined for scientific...Ch. 1 - Prob. 3CQCh. 1 - Prob. 4CQCh. 1 - Prob. 5CQCh. 1 - Prob. 6CQCh. 1 - Prob. 7CQCh. 1 - Prob. 8CQCh. 1 - Prob. 9CQCh. 1 - Prob. 10CQCh. 1 - Prob. 11CQCh. 1 - Prob. 12CQCh. 1 - Prob. 13CQCh. 1 - Prob. 14CQCh. 1 - Prob. 1MCQCh. 1 - Prob. 2MCQCh. 1 - Prob. 3MCQCh. 1 - Prob. 4MCQCh. 1 - Prob. 5MCQCh. 1 - Prob. 6MCQCh. 1 - Prob. 7MCQCh. 1 - Prob. 8MCQCh. 1 - Prob. 9MCQCh. 1 - Prob. 10MCQCh. 1 - Prob. 1PCh. 1 - Prob. 2PCh. 1 - Prob. 3PCh. 1 - Prob. 4PCh. 1 - Prob. 5PCh. 1 - On Monday, a stock market index goes up 5.00%. On...Ch. 1 - Prob. 7PCh. 1 - Prob. 8PCh. 1 - Prob. 9PCh. 1 - Prob. 10PCh. 1 - Prob. 11PCh. 1 - Prob. 12PCh. 1 - Prob. 13PCh. 1 - Prob. 14PCh. 1 - Prob. 15PCh. 1 - Prob. 16PCh. 1 - Prob. 17PCh. 1 - Prob. 18PCh. 1 - Prob. 19PCh. 1 - Prob. 20PCh. 1 - Prob. 21PCh. 1 - Prob. 22PCh. 1 - Prob. 23PCh. 1 - Prob. 24PCh. 1 - Prob. 25PCh. 1 - Prob. 26PCh. 1 - Prob. 27PCh. 1 - Prob. 28PCh. 1 - Prob. 29PCh. 1 - Prob. 30PCh. 1 - Prob. 31PCh. 1 - Prob. 32PCh. 1 - Prob. 33PCh. 1 - Prob. 34PCh. 1 - Prob. 35PCh. 1 - Prob. 36PCh. 1 - Prob. 37PCh. 1 - Prob. 38PCh. 1 - Prob. 39PCh. 1 - Prob. 40PCh. 1 - Prob. 41PCh. 1 - Prob. 42PCh. 1 - Prob. 43PCh. 1 - Prob. 44PCh. 1 - Prob. 45PCh. 1 - Prob. 46PCh. 1 - Prob. 47PCh. 1 - Prob. 48PCh. 1 - Prob. 49PCh. 1 - Prob. 50PCh. 1 - Prob. 51PCh. 1 - Prob. 52PCh. 1 - Prob. 53PCh. 1 - Prob. 55PCh. 1 - Prob. 56PCh. 1 - Prob. 57PCh. 1 - Prob. 58PCh. 1 - Prob. 59PCh. 1 - Prob. 60PCh. 1 - Prob. 61PCh. 1 - Prob. 62PCh. 1 - Prob. 63PCh. 1 - Prob. 64PCh. 1 - Prob. 65PCh. 1 - Prob. 68PCh. 1 - Prob. 69PCh. 1 - Prob. 70PCh. 1 - Prob. 71PCh. 1 - Prob. 72PCh. 1 - Prob. 73PCh. 1 - Prob. 74PCh. 1 - Prob. 75PCh. 1 - Prob. 76PCh. 1 - Prob. 77PCh. 1 - Prob. 78PCh. 1 - Prob. 79PCh. 1 - Prob. 80PCh. 1 - Prob. 81PCh. 1 - Prob. 82PCh. 1 - Prob. 83PCh. 1 - Prob. 84PCh. 1 - Prob. 85PCh. 1 - Prob. 86PCh. 1 - Prob. 87PCh. 1 - Prob. 88PCh. 1 - Prob. 89PCh. 1 - Prob. 90PCh. 1 - Prob. 91PCh. 1 - Prob. 92PCh. 1 - Prob. 93PCh. 1 - Prob. 94PCh. 1 - Prob. 95PCh. 1 - Prob. 96PCh. 1 - Prob. 97P
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