Scientific and Standard Notation with Applications

A rectangular section of land made up of wheat farms has a length of 5 x 10⁴ meters and a width of 6 x 10³ meters. What is the area of the land in square meters?

• 3 x 10⁶ meters

• 3 x 10⁷ meters

• 3 x 10⁸ meters

• 3 x 10¹² meters

A microscope is set so it makes an object appear 4 x 10² times larger than its actual size. A virus has a diameter of 2 x 10^-7 meter. How large will the diameter of the virus appear when it is viewed under the microscope?

• 8 x 10^-14

• 8 x 10^-5

• 8 x 10^-4

• 8 x 10⁵

Neptune is approximately 5 x 10⁴ kilometers in diameter. Mars is approximately 7 x 10³ kilometers in diameter. Which is an accurate comparison of the diameters of these two planets?

• The diameter of Neptune is more than 7 times greater than the diameter of Mars.

• The diameter of Mars is more than 7 times greater than the diameter of Neptune.

• The diameter of Neptune is about 1.4 times greater than the diameter of Mars.

• The diameter of Mars is about 1.4 times greater than the diameter of Neptune.

A box contains 5 x 10³ paper clips. The mass of each paper clip in the box is 8 x 10^-4 kilograms. What is the combined mass of the paper clips in the box?

• 4 kilograms

• 40 kilograms

• 4 x 10⁷ kilograms

• 4 x 10^-7 kilograms

One nanometer is equivalent to 1 x 10^-9 meter. Which is equivalent to 0.3 nanometers?

• -3 x 10¹⁰ meters

• -3¹⁰ meters

• 3 x 10^-9 meters

• 3 x 10^-10 meters

A rectangular yard has a length of 0.006 kilometers and a width of 5 x 10^-3 kilometers.

Use scientific notation to express the area of the yard in square kilometers.

• 3 x 10^-6 km²

• 3 x 10^-5 km²

• 30 x 10^-6 km²

• 3 x 10⁵ km²

Convert 3 x 10^-5 square kilometers into square meters using the conversion provided. Give your answer in standard form.

1 square kilometer (km²) = 1 x 10⁶ square meters (m²)

• 0.3 m²

• 3 m²

• 30 m²

• 300 m²

A farmer has a section of a field that measures 4 x 10³ feet by 5 x 10⁵ feet planted with carrots.

Another section is planted with corn measuring 6 x 10⁴ feet by 3 x 10⁴ feet.

What is the area of the carrot section? Write your answer in scientific notation.

• 20 x 10⁸ ft²

• 2 x 10⁸ ft²

• 2 x 10⁹ ft²

• 2⁹ ft²

A farmer has a section of a field that measures 4 x 10³ feet by 5 x 10⁵ feet planted with carrots.

Another section is planted with corn measuring 6 x 10⁴ feet by 3 x 10⁴ feet.

What is the area of the corn section? Write your answer in scientific notation.

• 9 x 10⁸

• 18 x 10⁸

• 1.8 x 10⁸

• 1.8 x 10⁹

A farmer has a section of a field that measures 4 x 10³ feet by 5 x 10⁵ feet planted with carrots.

Another section is planted with corn measuring 6 x 10⁴ feet by 3 x 10⁴ feet.

How much larger is the area of the carrot section than the corn section?

Select all that apply (HINT: there are TWO!).

• about 1.1 times larger

• 9 x 10^-1 ft² larger

• 2 x 10⁸ ft² larger

• about 9 times larger