WORKSHEET ON OPERATIONS WITH SCIENTIFIC NOTATION

Perform the indicated operations and simplify. The answer should be in scientific notation.

Problem 1 :

(1.2 × 10⁵) + (5.35 × 10⁶)

Solution

Problem 2 :

(6.91 × 10^-2) + (2.4 × 10^-3)

Solution

Problem 3 :

(9.70 × 10⁶) + (8.3 × 10⁵)

Solution

Problem 4 :

(3.67 × 10²) - (1.6 × 10¹)

Solution

Problem 5 :

(8.41 × 10^-5) - (7.9 × 10^-6)

Solution

Problem 6 :

(1.33 × 10⁵) - (4.9 × 10⁴)

Solution

Problem 7 :

According to scientists, the Earth's mass is 5.98 x 10²⁴ kilograms. The mass of the Sun is 1.989 x 10³⁰ kilograms. How much greater is the mass of the sun than the mass of the Earth ?

Solution

Problem 8 :

Last year, we noticed that the population of Tam worth was 5.6 x 10³. The population Liverpool was 1.3 x 10⁴. Which town had a larger population and by how much ?

Solution

Problem 9 :

How many times bigger is the distance from Earth to the sun of 9.3 x 10⁶ miles than the furthest distance from Earth to the moon of 3 x 10⁶ miles.

Solution

Problem 1 :

(4.3 × 10⁸) × (2.0 × 10⁶)

Solution

Problem 2 :

(6.0 × 10³) × (1.5 × 10^-2)

Solution

Problem 3 :

 (1.5 × 10^-2) × (8.0 × 10^-1)

Solution

Problem 4 :

(7.8 × 10³) / (1.2 × 10⁴)

Solution

Problem 5 :

(8.1 × 10^-2) / (9.0 × 10²)

Solution

Problem 6 :

(6.48 × 10⁵) / (2.4 × 10⁴)(1.8 × 10^-2)

Solution

Problem 7 :

A gigameter is 1.0 × 10⁶ kilometers. How many square kilometers are in 5 square gigameters?

Solution

Problem 8 :

The area of the Florida Keys National Marine Sanctuary is about 9.6 × 10³ square kilometers. The area of the Florida Reef Tract is about 16.2% of the area of the sanctuary. What is the area of the Florida Reef Tract in square kilometers?

Solution

Problem 9 :

There are about 1.4 × 10⁹ cubic kilometers of water on Earth. About 2.5% of the water is fresh water. How much fresh water is on Earth?

Solution

Problem 10 :

An album has sold 8,780,000 copies. How many more copies does it need to sell to receive the award?

a)  1.22 × 10⁻⁷    b) 1.22 × 10⁻⁶     c) 1.22 × 10⁶     d) 1.22 × 10⁷

Solution

Problem 11 :

Use a calculator to evaluate the expression. Write your answer in scientifi c notation and in standard form.

a. (1.5 × 10⁴) + (6.3 × 10⁴) 

 b. (7.2 × 10⁵) − (2.2 × 10³)

c. (4.1 × 10⁻³) × (4.3 × 10^{− 3}) 

d. ( 4.75 × 10^{− 6}) × (1.34 × 10⁷)

Solution

Convert Between Scientific Notation and Standard Form.

1)  5.3 × 10^{6         Solution}

2)  4.7 × 10^{-5             Solution}

3)  5 × 10^{4            Solution}

4)  4.59 × 10^{1          Solution}

5)  6.7 × 10^{4            Solution}

6)  9.6 × 10^{4         Solution}

7)  8.78 × 10^{3           Solution}

8)  5.82 × 10^{3          Solution}

9)  1.3 × 10^{5        Solution}

10)  4.1 × 10^{4        Solution}

11)  6.4 × 10^{2     Solution}

12)  6.91 × 10^{-2    Solution}

Problem 13 :

An object with a lesser density than water will float. An object with a greater density than water will sink. Use each given density (in kilograms per cubic meter) to explain what happens when you place a brick and an apple in water.

Water: 1.0 × 10³       Brick: 1.84 × 10³       Apple: 6.41 × 10

Solution

Problem 14 :

A dog has 100 female fleas. How much blood do the fleas consume per day?

Solution

Problem 15 :

Describe and correct the error in writing the number in standard form.

Solution

Problem 16 :

A googol is 1.0 × 10¹⁰⁰. How many zeros are in a googol?

Solution

Problem 17 :

The table shows the surface temperatures of five stars.

a. Which star has the highest surface temperature?

b. Which star has the lowest surface temperature?

Solution

Convert the following into scientific notation :

1)  92100     Solution

2)  0.000084    Solution

3)  700000        Solution

4)  9000     Solution

5)  9.03    Solution

6)  20     Solution

7)  0.000056    Solution

8)  0.0002         Solution

9)  4.12        Solution

10)  160       Solution

11) 0.66         Solution

Problem 12 :

Mercury’s distance from the Sun is approximately 5.79 × 10⁷ kilometers. What is this distance in standard form?

a) 5,790,000,000 km       b) 579,000,000 km

c)  57,900,000 km       d) 5,790,000 km

Solution

Problem 13 :

What is the diameter of a human hair written in scientific notation?

Solution

Problem 14 :

What is the circumference of Earth written in scientifi c notation?

Solution

Problem 15 :

The total power of a space shuttle during launch is the sum of the power from its solid rocket boosters and the power from its main engines. The power from the solid rocket boosters is 9,750,000,000 watts. What is the power from the main engines?

Solution

Problem 16 :

Write the number 0.853 in scientific notation.

Solution

Problem 17 :

0.36² in standard form is

(a) 0.01296 ×10¹      (b) 1.296 × 10^-1       (c) 0.1296 ×10⁰

(d) 12.96 ×10^-2

Solution