**Scientific notation word problems worksheet :**

Worksheet on scientific notation word problems is much useful to the students who would like to practice solving word problems on scientific notation.

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

2. When the Sun makes an orbit around the center of the Milky Way, it travels 2.025 × 10¹⁴ kilometers. The orbit takes 225 million years. At what rate does the Sun travel? Write your answer in scientific notation.

3. Light travels at a speed of 1.86 × 10⁵ miles per second. It takes light from the Sun about 4.8 × 10³ seconds to reach Saturn. Find the approximate distance from the Sun to Saturn. Write your answer in scientific notation.

4. Light travels at the speed of 1.17 × 10⁷ miles per minute. Pluto’s average distance from the Sun is 3,670,000,000 miles. On average, how long does it take sunlight to reach Pluto? Write your answer in scientific notation.

**Question 1 :**

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

**Answer :**

**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**

Using the population table in the last example, how many more people live in Mexico than in Canada ? Write your answer in scientific notation.

7.62 x 10⁷ more people live in Mexico than in Canada.

**Question 2 :**

When the Sun makes an orbit around the center of the Milky Way, it travels 2.025 × 10¹⁴ kilometers. The orbit takes 225 million years. At what rate does the Sun travel? Write your answer in scientific notation.

**Answer :**

**Key points : **

The answer is the number of kilometers per year that the Sun travels around the Milky Way.

Set up a division problem using

**Rate = Distance / Time **

to represent the situation.

**Step 1 : **

Substitute the values from the problem into the Rate formula.

**Step 2 : **

Write the expression for rate with years in scientific notation.

That is, 225 million = 2.25 x 10⁸

Then, we have

**Step 3 :**

Find the quotient by dividing the decimals and using the laws of exponents.

Divide the multipliers.

2.025 ÷ 2.25 = 0.9

Divide the powers of 10.

10¹⁴ ÷ 10⁸ = 10¹⁴ ⁻ ⁸

10¹⁴ ÷ 10⁸ = 10⁶

**Step 4 :**

Combine the answers to write the rate in scientific notation.

0.9 x 10⁶ = **9.0 x 10****⁵**

**Justify and Evaluate : **

Use estimation to check the reasonableness of your answer.

9.0 x 10⁵ is close 10⁶, so the answer is reasonable.

**Question 3 : **

Light travels at a speed of 1.86 × 10⁵ miles per second. It takes light from the Sun about 4.8 × 10³ seconds to reach Saturn. Find the approximate distance from the Sun to Saturn. Write your answer in scientific notation.

**Answer :**

As we have solved question 2, we can solve get answer for this question using the formula for distance given below.

**Distance = Speed x Time**

Then, we will get the answer : 8.928 × 10⁸ miles

**Question 4 :**

Light travels at the speed of 1.17 × 10⁷ miles per minute. Pluto’s average distance from the Sun is 3,670,000,000 miles. On average, how long does it take sunlight to reach Pluto? Write your answer in scientific notation.

**Answer :**

As we have solved question 2, we can solve get answer for this question using the formula for time given below.

**Time = Distance / Speed **

Then, we will get the answer : 3.14 × 10² minutes

After having gone through the stuff given above, we hope that the students would have understood "Scientific notation word problems worksheet".

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