MULTIPLYING AND DIVIDING WITH SCIENTIFIC NOTATION

About "Multiplying and dividing with scientific notation"

Multiplying and dividing with scientific notation :

We can multiply and divide numbers with scientific notation by using properties of exponents.

Multiplying and dividing with scientific notation - Examples

Example 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

Example 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 :

Use estimation to check the reasonableness of your answer. 9.0 x 10 is close 10so the answer is reasonable.

1)  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.

2)  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.

Answers for the above questions :

1)  8.928 × 10 miles

2)  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".

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