Math  /  Numbers & Operations

QuestionRuestion Completion Status: QUESTION 6 Perform the following operation. Answer using the appropriate number of significant figures // digits of precision. antilog 0.00654=0.00654= ?

Studdy Solution

STEP 1

1. The term "antilog" refers to the inverse operation of the logarithm.
2. The base of the logarithm is assumed to be 10, as it is the most common base used unless otherwise specified.
3. The problem requires the calculation to be performed to the appropriate number of significant figures based on the precision of the input value.

STEP 2

1. Understand the definition of antilog and its mathematical representation.
2. Convert the given logarithmic value to its antilogarithm.
3. Determine the appropriate number of significant figures for the result based on the precision of the input.

STEP 3

The antilog of a number x x is defined as 10x 10^x .
Therefore, we need to calculate: antilog(0.00654)=100.00654 \text{antilog}(0.00654) = 10^{0.00654}

STEP 4

Use a calculator or logarithm table to find the value of 100.00654 10^{0.00654} .
100.006541.0151 10^{0.00654} \approx 1.0151

STEP 5

Determine the appropriate number of significant figures for the final result.
Given the input 0.00654 0.00654 has 3 significant figures, we should report the result to 3 significant figures as well.
Therefore, the final result is: 1.015 1.015
Solution: The antilog of 0.00654 0.00654 is 1.015 1.015 when rounded to the appropriate number of significant figures.

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