Topic 2: Real Numbers

Rational/Irrational Numbers

100

Is the square root of 99 a rational or irrational number?

irrational

200

Which number is larger: square root of 82, or 9.1?

9.1

300

What is 0.4444444... as a fraction?

4/9

400

Put these numbers in order from smallest to largest:

9 1/2,  9.55555..., 9.8, square root of 94

9 1/2, 9.55555..., square root of 94, 9.8

500

What is 0.51515151... as a fraction? (Do not forget to simplify the fraction!)

17/33

Square/Cube Roots

100

What is the square root of 4?

2

200

What is the cube root of 125?

5

300

Is 100 a perfect square, perfect cube, neither, or both?

perfect square

400

Solve for x:

x²=64

x = +/- 8

500

Solve for x:

x³=81

x= cube root of 81

Properties of Exponents

100

Simplify: 

x¹⁴ * x¹⁶

x³⁰

200

Simplify:

x⁴⁰ / x²⁰

x²⁰

300

Simplify:

(x⁵)⁴

x²⁰

400

Make the exponent positive:

1 / x^-5

x⁵

500

Simplify and make sure the exponent is positive:

x¹² / x²⁶

1 / x¹⁴

Scientific Notation

100

What is 9,000 in scientific notation?

9 x 10³

200

What is 0.00085 in scientific notation?

8.5 x 10^-4

300

What is 95,817,420,000,000,000 in scientific notation?

9.581742 x 10¹⁶

400

Write 2.473 x 10¹² in standard form. Make sure to write your commas in!

2,473,000,000,000

500

Write 3.579 x 10^-10 in standard form.

0.0000000003579

Operations of Scientific Notation

100

(3 x 10²) x (2 x 10⁴)

6 x 10⁶

200

(6.4 x 10⁸) / (1.6 x 10⁴)

4 x 10⁴

300

(3.5 x 10⁶) x (8.2 x 10⁷)

2.87 x 10¹⁴

400

(5.3 x 10³) - (8 x 10²)

4.5 x 10³

500

(2.3 x 10⁶) + (1.6 x 10⁹)

1.6023 x 10⁹