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Match the items with their correct sizes. Can you write each size in Standard Form?
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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)