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Question: Antilog of the number \( ( - 8.654) \) is equal to A. \( 2.18 \times {10^{ - 8}} \) B. \( 2.18 ...

Antilog of the number (−8.654)( - 8.654) is equal to
A. 2.18×10−82.18 \times {10^{ - 8}}
B. 2.18×10−92.18 \times {10^{ - 9}}
C. 2.218×10−92.218 \times {10^{ - 9}}
D. 2.218×10−82.218 \times {10^{ - 8}}

Explanation

Solution

Hint : To find the antilog of the given number, as it is a negative decimal number so first convert the number such that it will have positive decimal numbers and then find the antilog value of that positive decimal from the antilog table. After finding the log number write it with multiplication with ten to the power of the negative digit left in the number.

Complete step by step solution:
In order to find the antilog value of the given negative number (−8.654)( - 8.654) , we will first express the number in two parts such that one part present decimal part and another the whole number, whereas we will convert negative decimal part into positive one with help of algebraic operation as follows
We can write (−8.654)( - 8.654) as
−8.654=−8−0.654- 8.654 = - 8 - 0.654
Adding and subtracting 11 , we will get
⇒−8.654=−8−0.654+1−1 ⇒−8.654=−8−1−0.654+1 ⇒−8.654=−9+0.346   \Rightarrow - 8.654 = - 8 - 0.654 + 1 - 1 \\\ \Rightarrow - 8.654 = - 8 - 1 - 0.654 + 1 \\\ \Rightarrow - 8.654 = - 9 + 0.346 \;
Now, we will find the value of 0.3460.346 in the antilog table, which will comes to be 2.2182.218
So writing it with in multiplication with ten to the power of negative nine, we will get the following value
⇒antilog(−8.654)=2.218×10−9\Rightarrow {\text{antilog(}} - 8.654) = 2.218 \times {10^{ - 9}}
Therefore this is the antilog value of the given number.
So, the correct answer is “Option C”.

Note : When solving objective type questions like this, try to remove wrong options with help of the negative whole number left after simplifying the given number. As we can see in this question, the negative whole number is minus nine, so we will see for the options having the power of ten equals negative nine and leaves all other options. This way will help you simplify the options.