Question

When \[3.8 \times {10^{ - 6}}\] is added to\[4.2 \times {10^{ - 5}}\] with due regard to significant figures, the result will be:
A) \[3.8 \times {10^{ - 5}}\]
B) \[0.458 \times {10^{ - 4}}\]
C) \[4.6 \times {10^{ - 5}}\]
D) \[8 \times {10^{ - 6}}\]

Answer 1

Hint: The given question deals with the concept of significant figures. In the question we are asked to add the given numbers together with due regard to significant figures. We know, significant numbers are the numbers that tell us about the accuracy of the number. So, we will assume the number as to different variables, add them both, take out the common factors, if any, and find the answer.

Complete step-by-step solution:
Now, let the given numbers be
\[{N_1} = 3.8 \times {10^{ - 6}}\]And \[{N_2} = 4.2 \times {10^{ - 5}}\]
Adding the two number, we get
\[ \Rightarrow {N_1} + {N_2} = {10^{ - 5}}\left\{ {\left( {3.8 \times {{10}^{ - 1}}} \right) + 4.2} \right\}\]
\[ \Rightarrow {10^{ - 5}}\left( {\dfrac{{3.8}}{{10}} + 4.2} \right)\]
\[ \Rightarrow {10^{ - 5}}\left( {\dfrac{{3.8 + 42}}{{10}}} \right)\]
\[ \Rightarrow {10^{ - 5}}\left( {\dfrac{{45.8}}{{10}}} \right)\]
\[ \Rightarrow {10^{ - 5}} \times 4.58\]\[ = 4.58 \times {10^{ - 5}}\]
\[ \Rightarrow 0.458 \times {10^{ - 4}}\]

Each of the non-zero digits are significant. The zeroes to the right of decimal after all significant digits are always non-significant. The zeroes to the left of the decimal between the non-zero digits are significant.

Therefore, the correct answer is option (B).

Note: Significant figures are non-zero digits that convey about the accuracy of a number. Example: 73 has two significant digits. Likewise, 0.00234 has three significant figures. They are, 2, 3 and 4 and zeroes tell us about the place values.