Q. 2.15 - An Introduction to General, Organic, and Biological Chemistry

Question

Write each of the following in scientific notation with two significant figures :

a. $5000 L$           b. $30 000 g$

c. $100 000 m$    d. $0.00025 cm$

Step-by-Step Solution

Answer

a. The scientific notation with two significant figures is $5.0\times {10}^3 L$           

b. The scientific notation with two significant figures is $3.0\times {10}^4 g$

c. The scientific notation with two significant figures is$1.0\times {10}^5 m$       

d. The scientific notation with two significant figures is$2.5\times {10}^{-4} cm$

Part (a) Step 1 : Given information

We have to write scientific notation of $5000 L$with two significant figures.

Part (a) Step 2 : Simplification

We know that, 

In $N\times {10}^M$ ( $N$ is significant and $M$ is the exponential term that only places the decimal point )

So, $5000 L = 5.0\times {10}^3 L$

Hence it has two significant figures.

Part (b) Step 1 : Given information

We have to write scientific notation of $30 000 g$ with two significant figures.

Part (b) Step 2 : Simplification

We know that, 

In $N\times {10}^M$ ( $N$ is significant and $M$ is the exponential term that only places the decimal point )

So, $30 000 g = 3.0\times {10}^4 g$

Hence it has two significant figures.

Part (c) Step 1 : Given information

We have to write scientific notation of $100 000 m$ with two significant figures.

Part (c) Step 2 : Simplification

We know that, 

In $N\times {10}^M$ ( $N$ is significant and $M$ is the exponential term that only places the decimal point )

So, $100 000 m = 1.0\times {10}^5 m$

Hence it has two significant figures.

Part (d) Step 1 : Given information

We have to write scientific notation of $0.00025 cm$ with two significant figures.

Part (d) Step 2 : Simplification

We know that, 

In $N\times {10}^M$ ( $N$ is significant and $M$ is the exponential term that only places the decimal point )

So, $0.00025 cm = 2.5\times {10}^{-4} cm$

Hence it has two significant figures.