Question

Express the following results to the proper number of significant figures: $\frac{\bigg( 1.308 \times 10^{-14}\bigg)(0.8)}{3.9}$

Answer 1

The following three rules are used to determine the number of significant numbers in a number:

• Non-zero numbers are always significant
• Any zeros between two significant numbers are significant.
• A “final zero” or “trailing zeros” only in the “decimal portion” are important. Examples: 0.900 or 0.928000 the zeros are significant.

$The\quad given\quad =\quad \frac { (1.308\quad \times \quad 10^{ -14 })(0.8) }{ 3.9 }$

In this calculation 0.8 has minimum “number” of “significant figures”.

It has only one significant figure.

The result of this calculation is, therefore, to be rounded off to one significant digit.

$\frac { (1.308\quad \times \quad 10^{ -14 })(0.8) }{ 3.9 } \quad =\quad \frac { 1.0464\quad \times \quad 10^{ -14 } }{ 3.9 } \quad =\quad 0.2683\quad \times \quad 10^{ -14 }$

Here, after 2 greater than 5. So, the result after rounding off is $0.3\quad \times\quad 10^{ -14 }$ and it has one significant figure.