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Calculate each of the following rounding to the number of digits shown . Further find the smallest interval using true values instead of rounded values, must lie :

(a) $ \ 23.46-12.753 \ $ and (b) $ \ 2.747*6.83 \ $

Answer:

(a)

$23.46-12.753 =10.707 $

What does mean it "round to the number of digits shown '' ?

Also how to find the smallest interval containing $ \ 10.707 \ $ .

Is it $ \ 10.707 \in [10.7070,10.7071) \ $ ?

MAS
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    The correct interval (if we use $3$ digits) is $[10.7065,10.7075)$ (The first value is included, the second excluded). In fact, the formulation "digits shown" is vague, I guess two digits because one number only has two digits. – Peter Sep 08 '17 at 13:14
  • why the interval $ [10.7070, 10.7071 ) $ is wrong ? – MAS Sep 08 '17 at 13:22
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    A number like $10.70749$ is rounded to $10.707$ (using $3$ digits), also $10.70651$ is rounded to $10.707$. So , your interval does not cover all cases – Peter Sep 08 '17 at 13:25
  • what about the second one ? $ 2.747*6.83=18.76201 \ $ Is the smallest interval $ 18.76201 \in [18.7620149, 18.7622051) $ ? – MAS Sep 08 '17 at 13:36
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    The correct interval in this case (using $5$ digits) is : $[18.762005,18.762015)$ – Peter Sep 08 '17 at 13:40

1 Answers1

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"Round to the number of digits shown" doesn't mean anything here! Either there would have to be a specific number of digits given separately or it should say "round to the smallest number of digits shown". A computation cannot be more accurate than the least accurate number in the calculation. It would appear that "23.46" is accurate to the "hundredths" place so the subtraction cannot be more accurate than 10.71. As for "the smallest interval containing 10.707", I suspect this is connected to the fact that we have measured to "hundredths place" and that the "true value" is somewhere between 10.7065 and 10.7075 since any number less than 10.7065 would be rounded down to 10.706 and any number larger than 10.7075 would be rounded up to 10.708.

user247327
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