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Find the percent error in each of the foll approximate to (pie=3.14) a) 22/7 b)355/113

asked
User Kongress
by
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1 Answer

5 votes

Explanation:

a)

we look at the ratio

22/7 / pi = 1.000402499...

as this is 1.x (100% + x%) of the full 100% of pi.

x is to be seen as

ab.cdefg... %

the first 2 digits are full % (as % is between 00 and 99). the following digits are fractions of %.

so,

1.000402499... = 100% + 00.0402499...%

that means, the percent error of 22/7 to real pi is about 0.0402499...% ≈ 0.04%

b)

the same for 355/113 :

355/113 / pi = 1.000000085...

the percent error of 355/113 to real pi is about 0.0000085...%

now, did your teacher really mean to approximate pi as 3.14 and compare the fractions and their accuracy to these 3.14 (instead of real pi) ?

then

a)

22/7 / 3.14 = 1.000909918...

the percent error of 22/7 to 3.14 (instead of real pi) is about 0.0909918...% ≈ 0.09%

b)

355/113 / 3.14 = 1.000507299...

the percent error of 355/113 to 3.14 (instead of real pi) is about 0.0507299...% ≈ 0.05%

answered
User Jamiecon
by
8.4k points

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