lesson objective revise how to write numbers using standard form

Lesson Objective

Revise how to write numbers using Standard Form

Understand what the notation for Standard Form Means

Begin to use a calculator to solve problems involving Standard Form

Match the items with their correct sizes.

Can you write each size in Standard Form?

A number written in Standard Form will always look like this:

a × 10n

Number here MUST be:

1 a < 10

Must always be written as × 10n

n is +ve for big numbers

n is –ve for small numbers

Important key facts about Standard Index Form

Write the number in the following form:

a × 10nNumber here MUST be:

1 ≤ a < 10

Must always be written as × 10n

n is +ve for big numbers

n is –ve for small numbers

Eg 6.23 × 105 = 623000

4.21 × 10-3 = 0.00421

(a)    Which planet has the largest diameter?

(1)

(b)    Which planet has the smallest diameter?

(1)

(c)    Which planet has a diameter approximately 10 times that of Venus?

(1)

(d)   Write 4.88 × 106 as an ordinary number.

(1)

(e)    What is the diameter of Pluto in kilometres?

Give your answer in standard form.

(2)

2.

1. Write these numbers in Standard Index Form:

a) 40 000 b) 120 000 c) 623 000 000

d) 0.000 05 e) 0.000 034 f) 6.2

g) 600 040 000 h) 0.256 i) 1.003

Using your calculator to solve problemsInvolving SI Form

Compare these two problems

1)A car travels 600 m in 84 seconds. What is its average speed during the journey?

2) A particle travels 5 × 108 m in

3 × 103 seconds what is the average speed of the particle during the journey?

Lesson Objective

Revise how to write numbers using Standard Form

Understand what the notation for Standard Form Means

Be able to do arithmetic without a calculator using Standard Form

Write this number in Standard Index form:

6 000 000

Write this number in Standard Index form:

72 000 000 000

Write this number in Standard Index form:

0.067

Write this number in Standard Index form:

0.000 000 032

Write this number in Standard Index form:

0.5

Write this number in Standard Index form:

10

Write this number in Standard Index form:

8

Write this number as a Decimal:

5.2 × 106

Find (without a calculator):

If a = 3 × 105

and b = 2 × 103

Write down the value of a × b in Standard Form

Find (without a calculator):

If a = 3 × 104

and b = 4 × 102

Write down the value of a × b in Standard Form

Find (without a calculator):

If a = 6 × 103

and b = 3 × 104

Write down the value of a × b in Standard Form

Find (without a calculator):

If a = 6 × 103

and b = 3 × 104

Write down the value of a + b in Standard Form

Find (without a calculator):

If a = 6 × 105

and b = 8 × 105

Write down the value of a + b in Standard Form

Find (without a calculator):

If a = 2.4 × 105

and b = 3 × 104

Write down the value of a + b in Standard Form

Find (without a calculator):

If a = 9 × 105

and b = 3 × 104

Write down the value of a ÷ b in Standard Form

Find (without a calculator):

If a = 12 × 108

and b = 4 × 105

Write down the value of a ÷ b in Standard Form

Find (without a calculator):

If a = 4 × 108

and b = 8 × 106

Write down the value of a ÷ b in Standard Form

Important key facts about Standard Index Form

Write the number in the following form:

a × 10nNumber here MUST be:

1 ≤ a < 10

Must always be written as × 10n

n is +ve for big numbers

n is –ve for small numbers

Eg 6.23 × 105 = 623000

4.21 × 10-3 = 0.00421

For S.I. Form without a calculator:

When multiplying and dividing use the normal index laws, but make certain the final answer is properly in S.I. Form

Eg. 7×104 × 3×105 = 21×109

= 2.1×1010

When adding and subtracting take the numbers out of S.I. Form (or at least adjust them so that the index is the same) then add/subtract as normal

Eg. 7×103 + 3×105 = 7×103 + 300×103

= 307×103

= 3.07×105

(or do 7000 + 300000 = 307000 = 3.07 ×105)

Let a = 3 × 106 b = 2 × 10-4 c = 5 × 107 d = 8 × 106

Find:

a) a × b

b) c2

c) a × c

d) d ÷ b

e) b ÷ d

f) a + d

g) a + c

h) a - c

Pick two different numbers and an

operation.

You capture the square if your calculation is

correct. Operation: + × ÷

Numbers: 4×105 3×107 2×106 1.2×108

8×10-6 9×10-3

1.2×1013

8×1011

4.8×1013

3.2×100

3.6×103

6×1013

3.6×1015

2.4×102

2.7×105

5×1010

2×10-11

3×102

3×10-10

1.6×101

2.5×1011

2.5×108

3.2×107

2.4×106

1.22×108

3.04×107

2.4×10146×101

2.5×10-8

1.5×101

9.008×10-3

Q2. For each calculation circle the answer that is correct and is in standard form.

(a)     (3 × 105) × (4 × 107)          Answers          12 × 1012      1.2 × 1036         12 × 1035            1.2 × 1013

(b)     (4 × 10–8) ÷ (8 × 10–2)          Answer          0.5 × 10–6     5 × 104            5 × 10–7              5 × 10–5

(Total 2 marks)