GATE CSE 2004 | Question: 28

Question

What is the result of evaluating the following two expressions using three-digit floating point arithmetic with rounding?

$(113. + -111.) + 7.51$

$113. + (-111. + 7.51)$

• A. $9.51$ and $10.0$ respectively

• B. $10.0$ and $9.51$ respectively

• C. $9.51$ and $9.51$ respectively

• D. $10.0$ and $10.0$ respectively

Comments

Rewrite the smaller number such that its exponent matches with the exponent of the larger number.

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@amarVashishth 

Do you mean smaller number in terms of magnitude without the sign ?  As in the accepted answer −1.11×10^2+7.51×10^0   ,  -1.11 (also -111 < 7.51)  is smaller than 7.51, but we are rewriting 7.51 's exponent to match with 1.11' s exponent

Answer 1

2^nd part:  113. + (-111. + 7.51)

(-111. + 7.51) = - .111 x 10³ + .751 x 10

= 10( - .111 x 10² + .751)

= 10(-11.1 + .751)

= 10(- 10.349)

= - 103.49

now, 113. + (- 103.49) = .113 x 10³ - .10349 x 10³ 

= 10³(.113 - .103)  // ignor 49 bcz  three-digit floating point arithmetic with rounding

= 10³ x .010

= 10