MULTIPLYING AND DIVIDING WITH SCIENTIFIC NOTATION WORKSHEET

Problem 1 :

Multiply :

(3.2 x 10⁵) x (2.67 x 10³)

Problem 2 :

Evaluate :

(2.688 x 10⁶) / (1.2 x 10²)

Problem 3 :

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.

Problem 4 :

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

Problem 5 :

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.

Detailed Answer Key

Problem 1 :

Multiply :

(3.2 x 10⁵) x (2.67 x 10³)

Solution :

=  (3.2 x 2.67) x (10⁵ x 10³)

=  (8.544) x (10⁵⁺³)

=  8.544 x 10⁸

The above number is in scientific notation. 

Therefore, 

(3.2 x 10⁵) x (2.67 x 10³)  =  8.544 x 10⁸

Problem 2 :

Evaluate :

(2.688 x 10⁶) / (1.2 x 10²)

Give your answer in scientific notation. 

Solution :

=  (2.688 / 1.2) x (10⁶ / 10²)

=  (2.24) x (10^6-2)

=  2.24 x 10⁴

Therefore, 

(2.688 x 10⁶) / (1.2 x 10²)  =  2.24 x 10⁴

Problem 3 :

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 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  =  10^14-8 

10¹⁴ ÷ 10⁸  =  10⁶ 

Step 4 :

Combine the answers to write the rate in scientific notation.

0.9 x 10⁶  =  9.0 x 10⁵

Justify and Evaluate : 

Use estimation to check the reasonableness of your answer.

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

Problem 4 :

Light travels at a speed of 1.86 x 10⁵ miles per second. It takes light from the Sun about 4.8 x 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

Problem 5 :

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

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