Operations in Scientific Notation

Scientific Notation

100

Is the following expression written in scientific notation? If not, explain why. 3.25+10^-7

No, 3.25 should be multiplied by 10^-7

200

The size of the Sahara desert is about 3.629*10⁶ square miles and the Arabian desert is about 9*10⁵ square miles. Which desert is larger? Explain how you know.

Sahara, because it has a larger exponent

300

The size of four oceans in square km is shown below. List the oceans from smallest to largest. Pacific Ocean: 1.796*10⁸, Artic Ocean: 1.323*10⁷, Atlantic Ocean: 1.061*10⁸, Indian Ocean: 7.498*10⁷

Artic, Indian, Atlantic, Pacific

400

Write a number in each missing exponent so that the equation is true and has at least one negative number.

2⁴ / 2^? = 2¹⁰

2^-6

Adding

100

Solve the expression (3.7*10⁹) + (9.04*10⁹)

1.274*10¹⁰

200

Solve (4.5*10⁴)+(1.75*10⁴)

6.25*10⁴

300

Solve (5.4*10³)+(1.2*10⁵)

1.254*10⁵

400

Earth has a mass 5.97 x 10²⁴ kg

Pluto has a mass of 13,000,000,000,000,000,000 kg

What is the total mass of Earth and Pluto?

5.983 x 10²⁴

Subtracting

100

Solve the expression (7*10⁵) - (5.2*10⁴)

6.48*10⁵

200

Solve (2*10⁴) - (4*10²)

1.96*10⁴

300

Solve (2.005*10⁵) - (8.664*10²)

1.996336*10⁵

400

Earth has a mass of 5.97 x 10²⁴ kg

Venus has a mass of 487 x 10²²

What is the difference between the mass of Earth and the mass of Venus?

1.1 x 10²⁴

500

Earth has a mass of 5.97 x 10²⁴ kg

Pluto has a mass of 13,000,000,000,000,000,000,000

Amoli says the mass of `100` Plutos is less than the mass of Earth.

Is her claim correct?

Yes. `100` Plutos would have a mass of 1.3 x 10²⁴ kg, which is less than the mass of Earth.

Multiplying

100

Solve the expression (4*10^-5)*(5*10¹²)

2*10⁸

200

Solve (6*10³)*(2*10⁵)

1.2*10⁹

300

Solve (5.1*10⁴)*(2.5*10³)

1.275*10⁸

400

Write a number in each missing exponent so that the equation is true and has at least one negative number.

5^? x 5^? = 5³

Answers vary but must use subtraction to equal 3

500

 person’s heart beats about 72 times each minute.

About how many times will a person’s heart beat in 80 years (about 4.2 × 10⁷ minutes)?

Write your answer in scientific notation.

3.024 × 10⁹ times in 80 years.

Dividing

100

Solve the expression (5.3*10⁶)/(4.2*10⁴)

1.26*10²

200

Solve (9*10⁸)/(2*10²)

4.5*10⁶

300

Solve (3.66*10^-5)/(2.0*10^-3)

1.83*10^-2

400

`8200000` is _______ times as large as `0.00041`. Write your answer in scientific notation.

2 x 10¹⁰

500

About 2.8×10⁷ people live in Texas.

About 5.6×10⁶ people live in Wisconsin.

Which number completes this sentence?

___ times as many people live in Texas as live in Wisconsin.

5