Download Scientific notation classnotes

Scientific notation classnotes
September 28, 2015
Find your new seat today.
You will need your laptop to begin.
Go to
https://todaysmeet.com/Scientificnotation
Which is the more important invention the telescope or the microscope?
Go to http://htwins.net/scale/
• Scale of the universe - zoom in and out and observe the numbers written in
scientific notation.
• Find one fact that is really small and one fact that is really big.
• Compare the two numbers.
• What is the difference between the two numbers? How did you calculate this?
• What rule do all numbers in scientific notation follow?
Scientific notation classnotes
September 28, 2015
http://syrianrefugees.eu/
6
x 10 Syrians have fled their homes since the outbreak of civil
An estimated 99 million
war in March 2.011x10
2011, taking refuge in neighbouring countries or within Syria itself.
According to the United Nations High Commissioner for Refugees (UNHCR), over 3
6
million
fled to Syria's immediate neighbours Turkey, Lebanon, Jordan and
3 x 10have
Iraq.
6.5 x
million
6.5
106 are internally displaced within Syria.
Meanwhile, under 1.5
150,000
x 105 Syrians have declared asylum in the European Union,
while member states have pledged to resettle a further 3.3
33,000
x 104Syrians.
The vast majority of these resettlement spots 2.85
28,500
x 104 or 85%
8.5 x 10 are pledged by
Germany.
3
Read this article and write the scientific notation as ordinary numbers.
Scientific notation classnotes
September 28, 2015
Calculations with scientific notation
Write in scientific notation and as ordinary numbers.
1) 450
2) 8792
3) 0.15
4) 0.045
3
5) 64 x 10
-5
6) 0.015 x 10
Scientific notation classnotes
Write in scientific notation
1)
2)
3)
4)
September 28, 2015
Write as an ordinary number
5)
6)
7)
8)
Write these correctly in standard form.
9)
10)
11)
12)
Order from least to greatest
13)
14)
Scientific notation classnotes
September 28, 2015
Calculating in scientific notation - Addition and Subtraction
When adding or subtracting numbers in scientific notation follow these steps:
1) Write each number in parentheses as an ordinary number.
for example
32000
4600
2) Add or subtract the two numbers.
32000
+ 4600 = 36600
3) Write the final answer in scientific notation.
36600 = 3.66 x 104
Scientific notation classnotes
September 28, 2015
Calculating in scientific notation - Addition and Subtraction
Using the example have a go at these questions:
1)
2)
3)
4)
5)
srewsnA
Scientific notation classnotes
September 28, 2015
Calculating in scientific notation - Multiplication
When multiplying numbers in scientific notation follow these steps:
1) Write each number in parentheses as an ordinary number.
for example
60000
200
2) multiply the two numbers.
200
x
60000 = 12000000
3) Write the final answer in scientific notation.
1200000 = 1.2 x 107
An alternative way would be:
1) Multiply the first number in the parentheses together.
2 x 6 = 12
2) Then multiply the base 10 in the parentheses together.
102 x 104 = 106
(from law of exponent an X am = an+m)
3) Combine the two answers together.
12 x 106
4) Then write the final answer in scientific notation.
12 x 106 = 1.2 x 107
Scientific notation classnotes
September 28, 2015
Calculating in scientific notation - Multiplication
Use both methods to answer these multiplications to check whether your answer is correct.
1)
2)
3)
4)
5)
Write down which method you prefer and why.
Scientific notation classnotes
September 28, 2015
Calculating in scientific notation - Division
When dividing numbers in scientific notation follow these steps:
1) Write each number in parentheses as an ordinary number.
for example
300
90000000
2) Divide the two numbers.
90000000 ÷ 300 = 300000
3) Write the final answer in scientific notation.
300000 = 3 x 105
An alternative way would be:
1) Divide the first number in the parentheses together.
9÷3=3
2) Then divide the base 10 in the parentheses together.
107 ÷ 102 = 105
(from law of exponent an ÷ am = an-m)
3) Combine the two answers together.
3 x 105
4) Then write the final answer in scientific notation.
5
3 x 10 is already in scientific notation
Scientific notation classnotes
September 28, 2015
Calculating in scientific notation - Division
Use both methods to answer these division to check whether your answer is correct.
1)
2)
3)
4)
5)
Write down which method you prefer and why.
Scientific notation classnotes
September 28, 2015
Calculations with scientific notation
Which number is smaller?
3.46 x 107 or 9.8 x 106
2.56 x 108 or 3.1 x 108
Explain why 4.2 x 10-5 is smaller than 3 x 10-4
Scientific notation classnotes
September 28, 2015
Calculations with scientific notation
Which number is smaller?
3.46 x 107 or 9.8 x 106
34600000
9800000
2.56 x 108 or 3.1 x 108
256000000
310000000
Explain why 4.2 x 10-5 is smaller than 3 x 10-4
0.000042
0.0003
Scientific notation classnotes
September 28, 2015
For each question write your answer in scientific notation
1) What is the difference between
4.67 x 103 and 4.5 x 102?
2) What is the sum of
52300 and 7.62 x 103?
3) What is (0.056)(2.2 x 102)?
Scientific notation classnotes
September 28, 2015
For each question write your answer in scientific notation
What is the difference between
1.243 x 107 and 1.0658 x 106?
What is the sum of 4.89 x 105 and 12000
What is (3 x 102)(2.56)?
Page 219
Qu 1, 3, 4, 5, 6
Scientific notation classnotes
Using Scientific Notation in Real Life Situations
September 28, 2015
Scientific notation classnotes
September 28, 2015
nucleus of a human cell is about 7 x 10-6 meter in diameter.
-8
A ribosome, another part of a cell, is about 3 x 10 meter in
The
diameter.
Approximately how many times larger is a nucleus than a ribosome?
7 x 10-6
3 x 10-8
= 2.33... x 102
Scientific notation classnotes
September 28, 2015
1.3 x 1025
27
The mass of Jupiter is about 4.2 x 10
The mass of Earth is about
About how many times Earth's mass is Jupiter's mass?
4.2 x 1027
1.3 x 1025
= 3.230... x 102
Scientific notation classnotes
September 28, 2015
Medium - answer questions 1, 3, 4, 6
Hard - answer questions 2, 5, 7
calculator
Difficult - answer questions 2, 5, 7
non-calculator
Scientific notation classnotes
September 28, 2015
Question 1
A pixel on a computer screen is 2 × 10–2 cm long by 7 × 10–3 cm wide.
What is the area of the pixel?
Question 2
The star Betelgeuse is 1.8 × 1015 miles from Earth. Light travels at 1.86 × 105 miles per second.
How many seconds does it take light to travel from Betelgeuse to Earth?
Give your answer in scientific notation.
Scientific notation classnotes
September 28, 2015
Question 3
A typical adult has about 20 000 000 000 000 red corpuscles. Each red corpuscle weighs about 0.000 000 000 1 gram. Write both of these numbers in scientific notation and work out the total mass of red corpuscles in a typical adult.
Question 4
Evaluate E M
­2
3
when E = 1.5 × 10 and M = 3 × 10 , giving your answer in scientific notation.
Question 5
Work out the value of
giving your answer in scientific notation, correct to two significant figures.
Scientific notation classnotes
September 28, 2015
Question 6
Many people withdraw money from their banks by using hole­in­the­wall machines. Each day there are eight million withdrawals from 32 000 machines. What is the average number of withdrawals
per machine?
Question 7
The mass of Saturn is 5.686 × 1026 tonnes. The mass of the Earth is 6.04 × 1021 tonnes. How many times heavier is Saturn than the Earth? Give your answer in standard form to a suitable degree of accuracy.
Scientific notation classnotes
September 28, 2015
Answers
Qu 1
2 x 10-2 x 7 x 10-3
(2 x 7) x (10-2x 10-3)
14 x 10-5
1.4 x 10-4
Qu 3
2 x 1013 x 1 x 10-10
(2 x 1) x (1013x 10-10)
2 x 103
Qu 2
1.8 x 1015 ÷ 1.86 x 105
(1.8 ÷ 1.86) x (1015÷ 105)
0.96774... x 1010
9.6774... x 109
Qu 4
1.5 x 103 ÷ 3 x 10-2
(1.5 ÷ 3) x (103÷ 10-2)
0.5 x 105
5 x 104
Qu 6
3.2 x 104 ÷ 8 x 106
(3.2 ÷ 8) x (104÷ 106)
0.4 x 10-2
4 x 10-3
Qu 5
3.2 x 107 ÷ 1.4 x 102
(3.2 ÷ 4) x (107÷ 102)
2.2857... x 105
2.3 x 105
Qu 7
5.686 x 1026 ÷ 6.04 x 1021
(5.686 ÷ 6.04) x (1026÷ 1021)
0.94139.. x 105
9.4139 x 104