# MULTIPLYING AND DIVIDING WITH SCIENTIFIC NOTATION WORKSHEET

## About "Multiplying and dividing with scientific notation worksheet"

Multiplying and dividing with scientific notation worksheet :

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

## Multiplying and dividing with scientific notation worksheet - Questions

1.  Multiply :

(3.2 x 10) x (26.7 x 10³)

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 × 10 5 miles per second. It takes light from the Sun about 4.8 × 10 3 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 × 10 7 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.

## Multiplying and dividing with scientific notation worksheet - Answers

Question 1 :

Multiply :

(3.2 x 10) x (26.7 x 10³)

Solution :

Step 1 :

Find the product of multipliers for each number.

3.2 x 26.7  =  85.44

Step 2 :

Find the product of powers of 10.

10⁵ x 10³  =  10

Step 3 :

Combine the results of step 1 and step 2 to write the final answer in scientific notation.

85.44 x 10  8.544 x 10

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.

Solution :

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 10

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.

10¹ ÷  10  =  10¹⁴ ⁻

10¹ ÷  10  =  10

Step 4 :

Combine the answers to write the rate in scientific notation.

0.9 x 10⁶  9.0 x 10

Justify and Evaluate :

9.0 x 10 is close 10so the answer is reasonable.

Question 3 :

Light travels at a speed of 1.86 × 10 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.

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 × 10 miles

Question 4 :

Light travels at the speed of 1.17 × 10 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.

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 "Multiplying and dividing with scientific notation worksheet".

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