Unit 2 Consolidation

Converting and Ordering in Scientific Notation

100

In this unit, scientific notation is also know as...

Standard Form

200

Convert 3,400,000 into scientific notation

3.4 x 10⁶

300

Convert 0.000241 into scientific notation

2.41 x 10^-4

400

Write the following in correct scientific notation:

45 x 10⁷

4.5 x 10⁸

500

Write the following in correct scientific notation:

0.0472 x 10^-4

4.72 x 10^-6

Operations in Scientific Notation

100

Calculate and write in correct standard form:
(2 x 10²) x (3 x 10²)

6 x 10⁴

200

Calculate and write in correct standard form:
(8 x 10⁵) ÷ (4 x 10⁴)

2 x 10¹

300

Calculate and write in correct standard form:

(6 x 10^-3) ÷ (3 x 10¹⁰)

2 x 10^-13

400

Calculate and write in correct standard form:

(6 x 10^-3) x (3 x 10¹⁰)

1.8 x 10⁸

500

Calculate and write in correct standard form:

13 x 3 x 10¹⁰⁴

3.9 x 10¹⁰⁵

Laws of Indices

100

Simplify:

a⁴ x a⁶

a¹⁰

200

Simplify:

y⁴⁰ ÷ y¹⁰

y³⁰

300

Simplify:

(4³)⁴

4¹²

400

Simplify:

(x^-5)^-6

x³⁰

500

Write as a single power of 2:

(2⁵ x 4³)²

2²²

Rational or Irrational?

100

Name a difference between a rational and an irrational number

Possible answers:

Rational numbers can be written as a fraction of two integers, whereas irrational numbers cannot.

Rational numbers have terminating or recurring decimals, whereas irrational numbers have non-terminating, non-recurring decimals.

Rational numbers include fractions, whereas irrational numbers cannot be expressed exactly as fractions.

200

Which of the following is irrational:

²/₅    -4    50    5.222...    π (pi)

π (pi)

300

Which of the following is rational?

√10    √25    √50    √20

√25 = 5 is an integer therefore it is rational

400

Which of the following is irrational?

√13   √25   √100   √196   √49

√13 is a square root of a non-squared number therefore it is irrational

500

Which of the following is rational?

√1220   √1225   √1205   √1250

√1225 = 35 is an integer therefore it is rational

Rounding, Approximations and Exact Values

100

Round the following to 2 decimal places:

36.9214

36.92

200

Give an approximation for the following irrational number with a degree of accuracy of 3 decimal places:

4π (4pi)

4π ≈ 4 × 3.142 = 12.568 (3 d.p)

300

Give an approximation for the following irrational number with a degree of accuracy of 3 decimal places:

√20

√20  ≈ 4.472 (3 d.p)

400

Give an approximation for the following irrational number with a degree of accuracy of 3 decimal places:

√29 - √3

≈ 5.385 − 1.732 = 3.653 (3 d.p)

500

(extension) Give the exact value of the following surd:

√75

√75 = √25 x √3 = 5√3