# OPERATIONS WITH SCIENTIFIC NOTATION WORKSHEET

## About "Operations with scientific notation worksheet"

Operations with scientific notation worksheet :

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

## Operations with scientific notation worksheet - Questions

1.  Simplify the expression given below.

(4x10⁵) + (0.1x10⁷)

2. Simplify the expression given below.

(0.123x10⁸) + (338.2x10⁵) - (7.1x10⁷)

3. Multiply :

(3.2 x 10) x (26.7 x 10³)

4.  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. ## Operations with scientific notation worksheet - Answers

Question 1 :

Simplify the expression given below.

(4x10⁵) + (0.1x10⁷)

Method 1 :

Step 1 :

In the given numbers, the highest power of 10 is 7.

So, write each number with 10 power 7.

4 x 10  =  0.04 x 10

0.1 x 10  =  0.1 x 10

Step 2 :

Add the multipliers for each number.

0.04 + 0.1  =  0.14

Step 3 :

Write the final answer in scientific notation :

0.14 x  10⁷   1.4 x 10

Method 2 :

Step 1 :

First, write each number in standard notation.

4 x 10  =  400,000

0.1 x  10  =  1,000,000

Step 2 :

Find the sum of the numbers in standard notation.

400,000 + 1,000,000  = 1,400,000

Step 3 :

Write the final answer in scientific notation :

1,400,000  =  1.4 x 10

Question 2 :

Simplify the expression given below.

(0.123x10⁸) + (338.2x10⁵) - (7.1x10⁷)

Method 1 :

Step 1 :

In the given numbers, the highest power of 10 is 8.

So, write each number with 10 power 8.

0.723 x 10⁸  =  0.723 x 10

338.2 x 10⁵  =  0.3382 x 10

6.1 x 10⁷  =  0.61 x 10

Step 2 :

Simplify the multipliers.

0.723 + 0.3382 - 0.61  =  0.4512

Step 3 :

Write the final answer in scientific notation :

0.4512 x 10⁸  =  4.512 x 10

Method 2 :

Step 1 :

First, write each number in standard notation.

0.723 x 10⁸  =  72,300,000

338.2 x 10⁵  =  33,820,000

6.1 x 10⁷  =  61,000,000

Step 2 :

Simplify the numbers in standard notation.

72,300,000 + 33,820,000 - 61,000,000  =  45,120,000

Step 3 :

Write the final answer in scientific notation :

45,120,000  =  4.512 x 10

Question 3 :

Multiply :

(3.2 x 10) x (26.7 x 10³)

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 4 :

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.

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. After having gone through the stuff given above, we hope that the students would have understood "Operations with scientific notation worksheet".

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