Scientific Notation

Exponents

100

8⁷ x 8³

8¹⁰

200

9¹⁰ / 9⁴

9⁶

300

(4⁵)⁶

4³⁰

400

(x⁹ / x²)³

x²¹

500

(a^b)^c

a^bc

Conversions

100

1,850,000

Convert to scientific notation.

1.85x10⁶

200

7.83x10⁷

Convert to standard form.

78,300,000

300

0.007826

Convert to scientific notation.

7.826x10^-3

400

5.138x10^-6

Convert to standard form.

0.000005138

500

0.000000083

Convert to scientific notation.

8.3x10^-8

Word Problems

100

Raul is aboard a cruise ship that weighs approximately 5.5x10⁷ pounds, while Veronica is aboard a cruise ship that weighs approximately 60,000,000 pounds. Whose cruise ship weighs more?

Veronica's cruise ship

200

Mr. Sanchez asked his students to write a value in scientific notation that was between 0.007 and 0.008. Natalie write the value 7.5x10^-3. Did she complete the task correctly? Why or or why not?

Yes, her answer in standard form is halfway between 0.007 and 0.008.

300

Raul is aboard a cruise ship that weighs approximately 5.5x10⁷ pounds, while Veronica is aboard a cruise ship that weighs approximately 60,000,000 pounds. How much heavier is the heaviest ship?

Heavier by 5,000,000 pounds

5x10⁶ pounds

400

Gabi is converting 0.000098 into scientific notation and has gotten 9.8x10^?. She does not know what the exponent should be. What should Gabi's exponent be?

The exponent should be -5

500

Dominic's science teacher wrote the wavelength for violet light on the board as 0.00004 cm. Dominic attempts to write the number in scientific notation and gets 0.4x10^-4. Is he correct? Why or why not?

No. His answer is not written in the correct form - his first term is not between 1 and 10.

Dividing

100

(8x10⁶)/(4x10³)

Answer in scientific notation

2x10³

200

(9x10⁹)/(3x10⁷)

Answer in scientific notation

2x10²

300

(10x10⁷)/(2x10²)

Answer in standard form

500,000

400

(5x10^-5)/(10x10^-2)

5x10^-4

500

(6x10^-3)/0.00003

Answer in standard form

200

Multiplying

100

(4.5x10⁵)(2x10³)

Answer in scientific notation

9x10⁸

200

(1.5x10^-5)(5x10^-3)

Answer in scientific notation

7.5x10^-8

300

(3x10⁴)(7.2x10²)

Answer in scientific notation

2.16x10⁷

400

(2.2x10^-2)(8.5x10⁶)

1.87x10⁵

500

(7.3x10^-1)(0.004)

Answer in standard form

0.00292