Q. 1.47 - An Introduction to General, Organic, and Biological Chemistry

Question

Write each of the following in scientific notation : $\left(1.5\right)$

a. $120 000$        b. $0.000 000 34$

c. $0.066$             d. $2700$

Step-by-Step Solution

Answer

a. The number $120 000$ in scientific notation is $1.2\times {10}^5$.

b. The number $0. 000 000 34$ in scientific notation is $3.4\times {10}^{\left(-7\right)}$.

c. The number $0.066$ in scientific notation is $6.6\times {10}^{\left(-2\right)}$.

d. The number $2700$ in scientific notion is $2.7\times {10}^{\left(3\right)}$.

Part (a) Step 1: Given Information

We need to write $120 000$ in scientific notation.

Part (a) Step 2: Explanation

First of all, moving the decimal place so the is only one number on the left side of the decimal point

$120 000 \to 1.20000$

Now, account for the movement using the powers of $10$, since we have moved five places to the left, we will include.

Part (b) Step 1: Given Information

We need to write $0.000 000 34$ in scientific notation.

Part (b) Step 2: Explanation

Firstly we will move the decimal place so there is only one number on the left side of the decimal point

$0.000 000 34\to 0000003.4$

Now, accounting for the movement using the power of $10$, since we have moved seven places to the right, we will include

 ${10}^{\left(-7\right)}=3.4\times {10}^{\left(-7\right)}$.

Part (c) Step 1: Given Information

We need to write $0.066$ in scientific notation.

Part (c) Step 2: Explanation

Firstly we will move the decimal place so there is only one number on the left side of the decimal point

$0.066\to 06.6$

Now, accounting for the movement using the power of $10$, since we have moved seven places to the right, we will include

${10}^{\left(-2\right)}=6.6\times {10}^{\left(-2\right)}$.

Part (d) Step 1: Given Information

We need to write $2700$ in scientific notation.

Part (d) Step 2: Explanation

Firstly we will move the decimal place so there is only one number on the left side of the decimal point

$2700\to 2.700$

Now, accounting for the movement using the power of  $10$, since we have moved seven places to the right, we will include

${10}^{\left(3\right)}=2.7\times {10}^{\left(3\right)}$.