Standard Form and Numbers Conversion
ζ
Standard Form
Dr Frost
Objectives:
Appreciate the need to put big and small numbers in a
more readable form, how to write numbers in standard form, and
calculations involving numbers in standard form.
Standard Form
A number between 1 and 10
(excluding 10)
Any whole number
(can be negative)
(No need to copy this)
Standard Form is useful for two reasons:
1.
It allows us to write really small or really big numbers concisely...
2.
It allows us to compare small and big numbers.
234000000000000
23400000000000
Which is bigger?!
Which is bigger?
2.34 x 10
14
2.34 x 10
13
On a calculator?
Converting from Standard Form
We just consider how many times we’re multiplying or dividing by 10.
3 x 10
4
= 30000
?
1.24 x 10
5
= 124000
?
6 x 10
-3
= 0.006
?
Hint:
Remember
what happens
when we have a
negative index.
1.01 x 10
-1
= 0.101
?
Converting from Standard Form
We just consider how many times we’re multiplying or dividing by 10.
3.012 x 10
7
= 30,120,000
?
7.5 x 10
1
= 75
?
8.31 x 10
0
= 8.31
?
2.4 x 10
-6
= 0.0000024
?
Converting
to
Standard Form
How many times do we need to move the decimal point until we’re in the
range 1 to 10? (excluding 10)
20000
= 2 x 10
4
?
0.0043
= 4.3 x 10
-3
?
931,000,000
= 9.31 x 10
8
?
0.000001001
= 1.001 x 10
-6
?
Exercises
Express in standard form.
Express as a normal number.
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Testing your knowledge (vote with your diary)
200,000,000
20 x 10
7
2 x 10
8
2 x 10
7
32,000
3.2 x 10
4
32 x 10
3
3.2 x 10
5
9
9 x 10
-1
9 x 10
0
9 x 10
1
0.0001
1 x 10
-3
1 x 10
-4
1 x 10
-5
0.012
1.2 x 10
-4
12 x 10
-3
1.2 x 10
-2
Multiplying numbers in standard form
(2 x 10
3
) x (4 x 10
4
)
= 8 x 10
7
?
?
(7 x 10
5
) x (6 x 10
6
)
= 42 x 10
11
= 4.2 x 10
12
?
?
Multiplying numbers in standard form
(9 x 10
-2
) x (9 x 10
-3
)
= 81 x 10
-5
= 8.1 x 10
1
x 10
-5
= 8.1 x 10
-4
?
?
?
= 5 x 10
6
Dividing numbers in standard form
?
= 0.5 x 10
7
= 5 x 10
-1
x 10
7
?
?
Dividing numbers in standard form
?
?
Edexcel GCSE Mathematics Textbook
Page 429 - Exercise 26B
Q4, 5
Page 432 – Exercise 26C
Q4, 5
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Explore the concept of standard form, learn how to write numbers concisely, and practice converting numbers to and from standard form through helpful examples and exercises. Enhance your skills in dealing with big and small numbers efficiently.
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Presentation Transcript
Dr Frost Standard Form Objectives: Appreciate the need to put big and small numbers in a more readable form, how to write numbers in standard form, and calculations involving numbers in standard form.
Scale of the Universe www.scaleofuniverse.com
Standard Form A number between 1 and 10 (excluding 10) Any whole number (can be negative) ? 10? (No need to copy this) Standard Form is useful for two reasons: 1. It allows us to write really small or really big numbers concisely... 2. It allows us to compare small and big numbers. Which is bigger?! Which is bigger? 2.34 x 1014 2.34 x 1013 234000000000000 23400000000000
On a calculator? 4.86 1021 2.88 109
Converting from Standard Form We just consider how many times we re multiplying or dividing by 10. 3 x 104 = 30000 1.24 x 105 = 124000 ? ? Hint: Remember what happens when we have a negative index. 6 x 10-3 = 0.006 1.01 x 10-1 = 0.101 ? ?
Converting from Standard Form We just consider how many times we re multiplying or dividing by 10. 3.012 x 107 = 30,120,000 7.5 x 101 = 75 ? ? 8.31 x 100 = 8.31 2.4 x 10-6 = 0.0000024 ? ?
Converting to Standard Form How many times do we need to move the decimal point until we re in the range 1 to 10? (excluding 10) 20000 = 2 x 104 0.0043 = 4.3 x 10-3 ? ? 931,000,000 = 9.31 x 108 0.000001001 = 1.001 x 10-6 ? ?
Exercises Express as a normal number. Express in standard form. ??? ? ? 300 = ? ??? 5,100 = ?.? ??? 72,040.4= ?.????? ??? 119,988.7= ?.?????? ??? 6,320,110= ?.????? ??? 8,108,136 = ?.?????? ??? 77,012 = ?.???? ??? 1.72= ?.?? ??? 34.7= ?.?? ??? 0.001 = ? ?? ? 0.00034 = ?.? ?? ? 0.9 = ? ?? ? 0.801 = ?.?? ?? ? 0.01087 = ?.??? ?? ? 0.00009 = ? ?? ? 0.00008632 = ?.??? ?? ? 0.11 = ?.? ?? ? ? 3 x 102 = ??? 4.71 x 103= ???? 2.401 x 105= ?????? 7.42 x 106= ??????? 1.1111 x 103= ????.? 1.5 x 10-1= ?.?? 3.01 x 10-4= ?.?????? 9.89 x 10-6= ?.???????? 3.456 x 10-7 = ?.?????????? 1.234 x 10-1= ?.???? ? ?? ?? ? ?? ?? ? ? ??? ??? ? ? ?
Testing your knowledge (vote with your diary) 200,000,000 20 x 107 2 x 108 2 x 107 32,000 3.2 x 104 32 x 103 3.2 x 105 9 9 x 10-1 9 x 100 9 x 101 0.0001 1 x 10-3 1 x 10-4 1 x 10-5 0.012 1.2 x 10-4 12 x 10-3 1.2 x 10-2
Multiplying numbers in standard form (2 x 103) x (4 x 104) = 8 x 107 ? ? (7 x 105) x (6 x 106) = 42 x 1011 = 4.2 x 1012 ? ?
Multiplying numbers in standard form (9 x 10-2) x (9 x 10-3) = 81 x 10-5 = 8.1 x 101 x 10-5 = 8.1 x 10-4 ? ? ?
Dividing numbers in standard form 4 105 8 10 2 = 0.5 x 107 = 5 x 10-1 x 107 ? ? = 5 x 106 ?
Dividing numbers in standard form 3 10 10 8 10 6 = 0.375 10 4 = 3.75 10 5 ? ?
Questions Edexcel GCSE Mathematics Textbook Page 429 - Exercise 26B Q4, 5 Page 432 Exercise 26C Q4, 5
Adding and Subtracting ? 1000 + 2000 = 3000 1 103+ 2 103= 3 103 ? 4 103+ 2 104 = 0.4 104+ 2 104 = 2.4 104 ? ?
Examples 1.1 105+ 2 104= 1.3 105 ? 1.1 105 2 104= 9 104 ? 5 107+ 2 105= 5.02 107 ? 6.2 10 2+ 3 10 3= 6.5 10 2 ? 9 1010+ 2 1012= 2.09 1012 ? 3.2 10 4 5 10 5= 2.7 10 4 ?
