**Adding and subtracting with scientific notation worksheet :**

Worksheet on adding and subtracting with scientific notation is much useful to the students who would like to practice problems on operations with scientific notation.

1. Simplify the expression given below.

(4x10⁵) + (0.1x10⁷)

2. Simplify the expression given below.

(0.123x10⁸) + (338.2x10⁵) - (7.1x10⁷)

3. The table below shows the population of the three largest countries in North America in 2011. Find the total population of these countries.

**Question 1 : **

Simplify the expression given below.

(4x10⁵) + (0.1x10⁷)

**Solution : **

**Method 1 :**

**Step 1 : **

In the given numbers, the highest power of 10 is 7.

So, write each number with 10 power 7.

4 x 10⁵ = 0.04 x 10⁷

0.1 x 10⁷ = 0.1 x 10⁷

**Step 2 : **

Add the multipliers for each number.

0.04 + 0.1 = 0.14

**Step 3 : **

Write the final answer in scientific notation :

0.14 x 10⁷ = ** 1.4 x 10****⁶**

**Method 2 :**

**Step 1 : **

First, write each number in standard notation.

4 x 10⁵ = 400,000

0.1 x 10⁷ = 1,000,000

**Step 2 : **

Find the sum of the numbers in standard notation.

400,000 + 1,000,000 = 1,400,000

**Step 3 : **

Write the final answer in scientific notation :

1,400,000 = **1.4 x 10****⁶**

**Question 2 : **

Simplify the expression given below.

(0.123x10⁸) + (338.2x10⁵) - (7.1x10⁷)

**Solution : **

**Method 1 :**

**Step 1 : **

In the given numbers, the highest power of 10 is 8.

So, write each number with 10 power 8.

0.723 x 10⁸ = 0.723 x 10⁸

338.2 x 10⁵ = 0.3382 x 10⁸

6.1 x 10⁷ = 0.61 x 10⁸

**Step 2 : **

Simplify the multipliers.

0.723 + 0.3382 - 0.61 = 0.4512

**Step 3 : **

Write the final answer in scientific notation :

0.4512 x 10⁸ = ** 4.512**** x 10⁷**

**Method 2 :**

**Step 1 : **

First, write each number in standard notation.

0.723 x 10⁸ = 72,300,000

338.2 x 10⁵ = 33,820,000

6.1 x 10⁷ = 61,000,000

**Step 2 : **

Simplify the numbers in standard notation.

72,300,000 + 33,820,000 - 61,000,000 = 45,120,000

**Step 3 : **

Write the final answer in scientific notation :

45,120,000 = **4.512 x 10⁷**

**Question 3 : **

The table below shows the population of the three largest countries in North America in 2011. Find the total population of these countries.

**Solution : **

**Method 1 :**

**Step 1 : **

First, write each population with the same power of 10.

United States : 3.1 x 10⁸

Canada : 0.338 x 10⁸

Mexico : 1.1 x 10⁸

**Step 2 : **

Add the multipliers for each population.

3.1 + 0.338 + 1.1 = 4.538

**Step 3 : **

Write the final answer in scientific notation :

** 4.538 x 10⁸**

**Method 2 :**

**Step 1 : **

First, write each number in standard notation.

United States : 310,000,000

Canada : 33,800,000

Mexico : 110,000,000

**Step 2 : **

Find the sum of the numbers in standard notation.

310,000,000 + 33,800,000 + 110,000,000 = 453,800,000

**Step 3 : **

Write the final answer in scientific notation :

453,800,000 = **4.538 x 10⁸**

After having gone through the stuff given above, we hope that the students would have understood "Adding and subtracting with scientific notation".

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