Question

Find the absolute error and the relative error in the product of 432.8 and 0.12584 using
four digit mantissa.​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

The absolute error and relative error in the product of the given numbers are 0.02376 and 4.364×10⁻⁴ respectively.

Step-by-step explanation:

Given:

x₁ = 432.8

x₂ = 0.12584

To find:

Absolute error and relative error in the product

Step 1:

The given numbers are 432.8 and 0.12584.

Since we have to use four-digit mantissa, we round off the second number to 0.1258

Step 2:

The product of these two numbers is given as

x = x₁ × x₂

x = 432.8 × 0.1258

x = 54.44624

Rounding off the product to four-digit mantissa, we get x = 54.47

Step 3:

The absolute error is given as follows:

Absolute error = |Approximate value - True value|

Absolute error = |54.47 - 54.44624|

Absolute error = 0.02376

Step 4:

The relative error is given as follows:

Relative error = Absolute error/True value

Relative error = 0.02376/54.44624

Relative error = 4.364×10⁻⁴

Therefore, the absolute error is 0.02376 and the relative error is 4.364×10⁻⁴.

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