Question

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

a. $5100000g$ b. $26000s$

c. $40000m$ d.$0.000820kg$

Short 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$8.2\times {10}^{-4}kg$

Step-by-step solution

Part (a) Step 1 : Given information

We have to write scientific notation of $5100000g$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, $5100000g=5.1\times {10}^{6}g$

Hence it has two significant figures.

Part (b) Step 1 : Given information

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

Hence it has two significant figures.

Part (c) Step 1 : Given Information

We have to write scientific notation of $40000m$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, $40000m=4.0\times {10}^{4}m$

Hence it has two significant figures.

Part (d) Step 1 : Given information

We have to write scientific notation of $0.000820kg$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, $0.000820kg=8.2\times {10}^{-4}kg$

Hence it has two significant figures.