Converting and Ordering in Scientific Notation
Operations in
Scientific Notation
Laws of
Indices
Rational or
Irrational?
Rounding, Approximations
and Exact Values
100

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

Standard Form

100

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

6 x 104

100

Simplify:

a4 x a6

a10

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.

100

Round the following to 2 decimal places:

36.9214

36.92

200

Convert 3,400,000 into scientific notation

3.4 x 106

200

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

2 x 101

200

Simplify:

y40 ÷ y10

y30

200

Which of the following is irrational:

2/5    -4    50    5.222...    π (pi)

π (pi)

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

Convert 0.000241 into scientific notation

2.41 x 10-4

300

Calculate and write in correct standard form:

(6 x 10-3) ÷ (3 x 1010)

2 x 10-13

300

Simplify:

(43)4

412

300

Which of the following is rational?

√10    √25    √50    √20

√25 = 5 is an integer therefore it is rational

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

Write the following in correct scientific notation:

45 x 107

4.5 x 108

400

Calculate and write in correct standard form:

(6 x 10-3) x (3 x 1010)

1.8 x 108

400

Simplify:

(x-5)-6

x30

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

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

Write the following in correct scientific notation:

0.0472 x 10-4

4.72 x 10-6

500

Calculate and write in correct standard form:

13 x 3 x 10104

3.9 x 10105

500

Write as a single power of 2:

(25 x 43)2

222

500

Which of the following is rational?

√1220   √1225   √1205   √1250

√1225 = 35 is an integer therefore it is rational

500

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

√75

√75 = √25 x √3 = 5√3

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