Suppose we approximate the value of 1/128 by rounding to 3 decimal places. a) what would be the approximation? b) what is the number of significant digits in the approximation? c) what is the absolute error? d) what is the relative error?

a) The approximation is 0.008.

b) One significant digit

c) The absolute error is 0.0001875

d) The relative error is of 2.4%.

Step-by-step explanation:

The formula for the absolute error is:

Absolute error = |Actual Value - Measured Value|

The formula for the relative error is:

Relative error = |Absolute error/Actual value|

The exact value of is 0.0078125

Rounded to 3 decimal places it is 0.008(since the fourth digit is 8, bigger than 5, the third digit is rounded up).

a) What would be the approximation?

The approximation is 0.008.

b) What is the number of significant digits in the approximation?

The approximation has one significant digit, that is, the number of digits that were changed by the approximation.

c) What is the absolute error?

The measured value is 0.008

The Actual value is 0.0078125

So

Absolute error = |Actual Value - Measured Value| = |0.0078125 - 0.008| = 0.0001875

d) What is the relative error?

The relative error is given by:

The relative error is of 2.4%.

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2

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step-by-step explanation:

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