Question

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

a. role="math" localid="1651689758670" $120000$ b. $0.00000034$

c. $0.066$ d. $2700$

Short answer

a. The number $120000$in scientific notation is localid="1652084498451" $1.2\times {10}^5$.

b. The number $0.00000034$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$2.7\times {10}^{\left(3\right)}$.

Step-by-step solution

Part (a) Step 1: Given Information

We need to write$120000$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

$120000\to 1.20000$

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$0.00000034$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

$0.00000034\to 0000003.4$

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

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