# 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 (106-2)

=  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  =  1014-8

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 106so 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 × 10 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 Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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