1. Lab Skills and Chemical Analysis
S3 UNIT 1
Lab Skills and Chemical Analysis
Scientific Notation

2. Scientific Notation
Context for learning: Scientific notation allows you to write and work with very large or very small numbers without having to write loads of zeros.
Learning Intentions (WALT):
We are learning to:
Write really big and really small numbers in scientific notation.
Complete calculations with numbers written in scientific notation
Adding and subtracting
Dividing and multiplying
Extension
Understand the zero power rule
Success Criteria(WILF):
What I’m looking for:
Be able to convert easily from a number to scientific notation and vice versa.
Be able to carry out calculations using scientific notation for real-life examples.
Extension
Be able to explain using mathematical examples why any number raised to the power of 0 is 1.

3. New words Meaning GLOSSARY Index (powers) (exponent)
The index of a number says how many times to use the number in a multiplication. It is written as a small number to the right and above the base number. In this example: 82 = 8 × 8 = 64. The plural of index is indices. (Other names for index are exponent or power.)
Scientific notation (standard form)
Scientific notation is the way that scientists easily handle very large numbers or very small numbers. For example, instead of writing , we write 5.6 x 10-9.
Coefficient
A number used to multiply a variable.
Decimal System
So, our Decimal System lets us write numbers as large or as small as we want, using the decimal point. Digits can be placed to the left or right of a decimal point, to show values greater than one or less than one. The decimal point is the most important part of a Decimal Number.

4. Indices
Indices are also called Powers or Exponents, they are used as a means of writing repeated calculations in a shorter way.

5. Scientific Notation
Scientific notation is the way that scientists easily handle very large numbers or very small numbers. For example, instead of writing , we write 5.6 x 10-9.

6. Very large number Very small number
Scientific Notation
Very large number
Very small number
Mass of the sun is: kg
Mass of a proton: kg

7. The mass of one gold atom is .000 000 000 000 000 000 000 327 grams.
Scientific Notation is used to express the very large and the very small numbers so that problem solving will be made easier.
Examples:
The mass of one gold atom is
grams.
One gram of hydrogen contains
hydrogen atoms.
Scientists can work with very large and very small numbers more easily if the numbers are written in scientific notation.

8. How to Use Scientific Notation
In scientific notation, a number is written as the product of two numbers…..
…..a coefficient and 10 raised to a power.

9. For example: 4.5 x 103 The coefficient is _________. 4.5
The number 4,500 is written in scientific notation as ________________.
The coefficient is _________.
4.5
The coefficient must be a number greater than or equal to 1 and smaller than 10.
The power of 10 or exponent in this example is ______. 3
The exponent indicates how many times the coefficient must be multiplied by 10 to equal the original number of 4,500.

10. Very large numbers!
BOOM!
92,000,000 miles
How far?

11. Very large numbers! SPLAT! How many seconds in 70 years?
Happy 70th Birthday!
How many seconds in 70 years?
SPLAT!
70 years = seconds!

12. Dinosaurs roamed the earth 228 million years ago
Very large numbers!
Dinosaurs roamed the earth 228 million years ago

13. Short hand! 10
100 = 10 x 10
1 000 = 10 x 10 x 10
= 10 x 10 x 10 x 10
= 10 x 10 x 10 x 10 x 10
= 10 x 10 x 10 x 10 x 10 x 10

14. Scientific Notation This is also known as Standard form. 200 = 2 x 100

15. Exercise 1
2 000
(2)
(3) 500
(4)
(5)
= 2 x 1000
= 2 x
= 5 x 100
= 8 x
= 9 x

16. A short cut 8 000 000 . . Move the point to get a
number between 1 and 10
The point moved 6 places . .
Add the
decimal point
Between 1 and 10

17. A short cut 92 000 000 . . Move the point to get a
number between 1 and 10
The point moved 7 places . .
Add the
decimal point
Between 1 and 10

18. Happy Birthday: Seconds old!
A short cut
Move the point to get a
number between 1 and 10
The point moved 9 places . .
Add the
decimal point
Between 1 and 10
Happy Birthday: Seconds old!
SPLAT!

19. A short cut 228 000 000 . . Move the point to get a
number between 1 and 10
The point moved 8 places . .
Add the
decimal point
Between 1 and 10

20. Exercise 2
(1)
(2)
(3) 5 300
(4)
(5)
(6)
(7)
(8)
(9)
(10)

21. Add 7 zeros, although you probably won’t need them all.
Changing back
The point moves 7 places
8.6 . =
Hint:
Add 7 zeros, although you probably won’t need them all.
Zeros after the point aren’t needed.

22. Add 5 zeros, although you probably won’t need them all.
Changing back
The point moves 5 places
3.46
00000 . =
Zeros after the point aren’t needed.
Hint:
Add 5 zeros, although you probably won’t need them all.

23. Exercise 3
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10) =
= 8 000 = = = = = = = =

24. Name that number!
1 000
What’s this called?
one thousand
What’s this called?
one million
and this one?
one billion
one googol !!!
What’s this called?

25. Very small numbers!
How wide is an atom?
metres wide!

26. Standard Form for small numbers
Move the point to get a
number between 1 and 10 .
The point moved 10 places. Negative sign for small numbers.

27. Standard Form for small numbers
Move the point to get a
number between 1 and 10 .
The point moved 7 places. Negative sign for small numbers.

28. Standard Form for small numbers
Move the point to get a
number between 1 and 10 .
The point moved 6 places. Negative sign for small numbers.

29. Exercise 4
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)

30. Changing back small numbers Add 3 zeros to the left of the number.
-3 so remember to move point left for small numbers.
Hint:
Add 3 zeros to the left of the number.
000 . 2 .
= 0.002

31. Changing back small numbers Add 5 zeros to the left of the number.
-3 so remember to move point left for small numbers.
Hint:
Add 5 zeros to the left of the number.
00000 .
8.6 =

32. Changing back small numbers Add 6 zeros to the left of the number.
-3 so remember to move point left for small numbers.
Hint:
Add 6 zeros to the left of the number.
000000 .
5.16 =

33. Exercise 5
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10) = = = = = = = = = =

34. Rules to Remember!
If a number is greater than 10, the exponent will be _____________ and is equal to the number of places the decimal must be moved to the ________ to write the number in scientific notation.
positive
left
If a number is less than 10, the exponent will be _____________ and is equal to the number of places the decimal must be moved to the ________ to write the number in scientific notation.
negative
right

35. A number will have an exponent of zero if:
….the number is equal to or greater than 1, but less than 10.

36. 1. Move the decimal to the right of the first non-zero number.
To write a number in scientific notation:
1. Move the decimal to the right of the first non-zero number.
2. Count how many places the decimal had to be moved.
3. If the decimal had to be moved to the right, the exponent is negative.
4. If the decimal had to be moved to the left, the exponent is positive.

37. Practice Problems ANSWERS PROBLEMS 1.2 x 10-4 1 x 103 1 x 10-2
Put these numbers in scientific notation.
PROBLEMS
1.2 x 10-4
1 x 103
1 x 10-2
1.2 x 101
9.87 x 10-1
5.96 x 102
7.0 x 10-7
1.0 x 106
1.26 x 10-3
9.88 x 1011
8 x 100
ANSWERS
.00012
1000
0.01 12
.987
596
1,000,000
987,653,000,000 8

38. EXPRESS THE FOLLOWING AS WHOLE NUMBERS OR AS DECIMALS
PROBLEMS
ANSWERS
4.9 X 102
3.75 X 10-2
5.95 X 10-4
9.46 X 103
3.87 X 101
7.10 X 100
8.2 X 10-5
490
.0375
9460
38.7
7.10

39. In the United States, 15,000,000 households use private wells for their water supply. Write this number in scientific notation. 1.5 X 107

40. The U.S. has a total of X 107 acres of land reserved for state parks. Write this in standard form.
12,916,000 acres

41. .000007 meters The nucleus of a human cell is about 7 X 10-6
meters in diameter. What is the length in
Scientific notation?
meters

42. A ribosome, another part of a cell, is about 0
A ribosome, another part of a cell, is about of a meter in diameter. Write the length in scientific notation. 3 X 10-9

43. Using Scientific Notation in Multiplication, Division, Addition and Subtraction
Scientists must be able to use very large and very small numbers in mathematical calculations. As a student in this class, you will have to be able to multiply, divide, add and subtract numbers that are written in scientific notation. Here are the rules.

44. Sample Problem: Multiply (3.2 x 10-3) (2.1 x 105)
Multiplication
When multiplying numbers written in scientific notation…..multiply the coefficients and add the exponents.
Sample Problem: Multiply (3.2 x 10-3) (2.1 x 105)
Solution: Multiply 3.2 x Add the exponents
Answer: 6.7 x 102

45. Sample Problem: Divide (6.4 x 106) by (1.7 x 102)
Division
Divide the numerator by the denominator. Subtract the exponent in the denominator from the exponent in the numerator.
Sample Problem: Divide (6.4 x 106) by (1.7 x 102)
Solution: Divide 6.4 by Subtract the exponents 6 - 2
Answer: 3.8 x 104

46. Multiplication and Division

47. Addition and Subtraction
To add or subtract numbers written in scientific notation, you must….express them with the same power of ten.
Sample Problem: Add (5.8 x 103) and (2.16 x 104)
Solution: Since the two numbers are not expressed as the same power of ten, one of the numbers will have to be rewritten in the same power of ten as the other.
5.8 x 103 = .58 x so .58 x x 104 =?
Answer: x 104

48. Addition and Subtraction

49. Scientific notation and your calculator

50. Kahoot
Scientific Notation