Q. 2.16 - An Introduction to General, Organic, and Biological Chemistry

Question

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

a. $5100 000 g$             b. $26000 s$

c. $40 000 m$                 d. $0.000 820 kg$

Step-by-Step Solution

Answer

a. The scientific notation with two significant figures is $5.1\times {10}^6 g$          

b. The scientific notation with two significant figures is $2.6\times {10}^4 s$

c. The scientific notation with two significant figures is $4.0\times {10}^4 m$

d. The scientific notation with two significant figures is $8.2\times {10}^{-4} kg$

Part (a) Step 1 : Given information

We have to write scientific notation of $5100 000 g$ 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, $5100 000 g = 5.1\times {10}^6 g$

Hence it has two significant figures.

Part (b) Step 1 : Given information

We have to write scientific notation of $26000 s$ 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, $26000 s = 2.6\times {10}^4 s$

Hence it has two significant figures.

Part (c) Step 1 : Given Information

We have to write scientific notation of $40 000 m$ 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, $40 000 m = 4.0\times {10}^4 m$

Hence it has two significant figures.

Part (d) Step 1 : Given information

We have to write scientific notation of $0.000 820 kg$ 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, $0.000 820 kg = 8.2\times {10}^{-4} kg$

Hence it has two significant figures.