Q1.64P - Chemistry: Molecular Nature Of Matter And Change

Question

Convert the following into correct scientific notation: 

(a)  $\mathbf{802}\mathbf{.}\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{2}}$

(b)  $\mathbf{1009}\mathbf{.}\mathbf{8}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{6}}$

(c) $\mathbf{0}\mathbf{.}\mathbf{077}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{9}}$

Step-by-Step Solution

Answer

The answer is,

(a) $8.025\times {10}^4$

(b) $1.0098\times {10}^{-3}$

(c) $7.7\times {10}^{-11}$

Step 1: Scientific Notation

The scientific notation is used for the representation of larger or very small numbers using decimals, powers and integer numbers. The numbers or digits are shifted towards either left or right of the decimal point.

Step 2: Subpart (a)

The number  $802.5\times {10}^2$  can be written in correct scientific notation as  $8.025\times {10}^4$. This involves the shifting of two digits to the right with respect to the decimal.

Step 3: Subpart (b)

The number $1009.8\times {10}^{-6}$ can be written in correct scientific notation as $1.0098\times {10}^{-3}$. This involves the shifting of three digits to the right with respect to the decimal.

Step 4: Subpart (c)

The number $0.077\times {10}^{-9}$  can be written in correct scientific notation as $7.7\times {10}^{-11}$ . This involves the shifting of two digits to the left with respect to the decimal.