Multiple Choice Questions on Errors and Floating-Point

Multiple Choice Questions on Errors and Floating-Point. We have discussed the questions based on significant numbers, round off, truncation, measures of errors, normalized floating-point, and arithmetic operations on normalized floating points.

MCQ ON THE SOLUTION OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS:

MCQ on the solution of algebraic and transcendental equations are discussed here with answers underlined. You can test your knowledge. 

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Question 1: Round off the number 5.9154 up to 3 decimal places

A) `5.915`

B) `5.916`

C) `5.91`

D) None

Explanation: `5.915`.

Question 2: Truncation errors are caused by

A) Rounding off

B) Both rounding and replacing one

C) Replacing an infinite process to finite one

D) None

Explanation: Replacing an infinite process to finite one

Question 3: Absolute error is given by

A) `|True value - Approximate value|`

B) `|True value + Approximate value|`

C) Both

D) None

Explanation: `|True value - Approximate value|`.

Question 4: Accuracy relates to

A) No. of significant figures

B) No. of rounding off figures

C) Both

D) None

Explanation: No. of significant figures

Question 5: Which of the following are measures of errors

A) Absolute error

B) Relative error

C) Percentage error

D) All

Explanation: All

Question 6: The number of significant digits in the number 204.020050

A) 9

B) 6

C) 8

D) 5

Explanation: 9

Question 7: Find relative error if 2/3 is approximated to 0.667.

A) `-0.005`

B) `-0.05`

C) `-0.5`

D) `-0.0005`

Explanation: `-0.0005`

Question 8: The height of a tower as 47 m whereas its actual height is 45m. Calculate the relative error?

A) `0.04444`

B) `0.444`

C) `4.4444`

D) None

Explanation: `0.04444`

Question 9: The number 305.007 has significant digits.

A) 3

B) 4

C) 5

D) 6

Explanation: 6

Question 10: The percentage error is given by

A) `Relative error \times 100`

B) `\frac{Relative error} {100}`

C) `Relative error \times 1000`

D) None

Explanation: Newton Raphson Method

Question 11: Inherent errors are

A) Already present in statement

B) Caused by rounding off

C) Both

D) None

Explanation: Already present in statement

Question 12: Number of significant figures in number 208.0

A) 3

B) 2

C)4

D) None

Explanation: 3

Question 13: In which of the following numerical values, all zeroes are significant

A) 2002

B) 200

C) 0.0002

D) None

Explanation: 2002

Question 14: Rounding off the number 32.68673 to 4 significant digits, we get a number

A) `32.67`

B) `32.69`

C) None

D) `32.686`

Explanation: `32.69`

Question 15: The significant figures of the number 6.0023 is

A) 5

B) 3

C) 4

D) 1

Explanation: 5.

Question 16: If percentage error of a number is `3.264 \times 10^-4` then its relative error is

A) `3.264 \times 10^{-6}`

B) `3.264 \times 10^{-2}`

C) Is `3.264 \times 10^{-5}`

D) None

Explanation: `3.264 \times 10^{-6}`

Question 17: Find the absolute error of ` 2^{\frac{1}{2}} `

A) `0.00001`

B) `0.00002`

C) `0.00005`

D) None

Explanation: `0.00001`

Question 18: Relative error is given by

A) `\frac{X-X'}{X}`

B) `\frac{X-X'}{X+X'}`

C) `\frac{X+X'}{X}`

D) None

Explanation: `\frac{X-X'}{X}`

Question 19: Suppose 1.414 is used as an approximate value to `\sqrt{2}`. Find the absolute error

A) `0.21356 \times 10^{-3}`

B) `1.21356 \times 10^{-3}`

C) `0.21356 \times 10^{-6}`

D) None

Explanation: `0.21356 \times 10^{-3}`

Question 20: Suppose 1.414 is used as an approximate value to `\sqrt{2}`. Find the relative error

A) `0.151 \times 10^{-3}`

B) `0.21356 \times 10^{-6}`

C) `1.21356 \times 10^{-6}`

D) None

Explanation: `0.151 \times 10^{-6}`

Question 21: Suppose 1.414 is used as an approximate value to `\sqrt{2}`. Find the percentage error

A) `0.151 \times 10^{-1}`

B) `0.21356 \times 10^{-6}`

C) `1.21356 \times 10^{-6}`

D) None

Explanation: `0.151 \times 10^{-1}`

Question 22: Round off the number 75462 to four significant digits

A) 75460

B) 75400

C) 75500

D) None

Explanation: 75460

Question 23: Round off the number 75462 to four significant digits, then its absolute error is

A) `2`

B) `2.6`

C) `3`

D) None

Explanation: `2`.

Question 24: Round off the number 75462 to four significant digits, then its relative error is

A) `0.0000265`

B) `0.0000265567`

C) `0.0000865`

D) None

Explanation: `0.0000265`

Question 25: Round off the number 75462 to four significant digits, then its percentage error is

A) `0.00265`

B) `0.00865`

C) `0.00265678`

D) None

Explanation: `0.00265`

Question 26: Round off the number 37.46235 to four significant figures

A) `37.4623`

B) `37.4`

C) `37.46`

D) None

Explanation: `37.46`

Question 27: Truncate the number 37.43523 to four significant figures.

A) ` 37.43`

B) `37.44`

C) `37.435`

D) None

Explanation: `37.43`.

Question 28: Round off the number 37.46235 to four significant figures and compute absolute error

A) `0.000235`

B) `0.0235`

C) `0.00235`

D) None

Explanation: `0.00235`

Question 29: Find the absolute error if X is rounded off to three decimal digits as `X=0.005998`

A) `0.012345`

B) `0.0002`

C) `0.02345`

D) `0.000002`

Explanation: `0.000002`

Question 30: Rounded off to three decimal digits as `X= 0.005998`

A) 0.006

B) 0.06

C) 0.005987

D) None

Explanation: 0.006

Question 31: Find the relative error if X is rounded off to three decimal digits as `X= 0.005998`

A) 0.00333

B) 0.2345

C) 0.02345

D) None

Explanation: 0.00333

Question 32: Find the percentage error if X is rounded off to three decimal digits as `X= 0.005998`

A) 0.33344

B) 0.0033444

C) 0.0056456

Explanation: 0.33344

Question 33: Errors may occur in performing numerical computation on the computer due to

A) rounding off

B) power fluctuation

C) operation

D) All

Explanation: Rounding off

Question 34: If X is the true value and X' is an approximate value then the formula `|X-X'|`

A) relative error

B) percentage error

C) Absolute error

D) None

Explanation: absolute error

Question 35: If X is the true value and X' is an approximate value then the formula `\frac{|X-X'|}{X}`

A) Relative error

B) Absolute error

C) percentage error

D) None

Explanation: Relative error.

Question 36: If X is the true value and X' is an approximate value then the formula `\frac{|X-X'|}{X} \times 100`

A) percentage error

B) Relative error

C) Absolute error

D) None

Explanation: 7

Question 37: To round off a number to n significant digits, and if this discarded number is less than 5 then

A) `n^th ` digit unaltered

B) `n^th `digit increased by 1

C) `n^th `digit increased by 0.5

D) None

Explanation: `n^th ` digit unaltered

Question 38: To round off a number to n significant digits, and if this discarded number is greater than 5 then

A) `n^th ` digit unaltered

B) `n^th `digit increased by 0.5

C) `n^th `digit increased by 1

D) None

Explanation: `n^th `digit increased by 1

Question 39: To round off a number to n significant digits, and if this discarded number is exactly 5 then nth digit unaltered

A) If it is an odd number

B) If it is an even number

C) Can't say

D) None

Explanation: If it is an odd number

Question 40: To round off a number to n significant digits, and if this discarded number is exactly 5 then nth digit incresed by 1

A) If it is an even number

B) If it is an odd number

C) Can't say

D) None

Explanation: If it is an even number

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Total Questions Attempted: 0

Correct Answers: 0

Wrong Answers: 0

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