measurements in physics it is the first topic to discuss

1. Sir Melo
Scientific notation, also called
exponential notation, is a convenient
way of writing values using the power of
ten notation wherein we can determine
the number of significant digits as well
as the place value of the digit. Place
values are denoted by prefixes.
Scientific Notation

2. Sir Melo
Format: 𝐶. 𝑀𝑀𝑀𝑀𝑀 × 10𝑒
where: 𝐶 - the characteristic digit, may be any digit from 0-9
𝑀 – the mantissa digits, may be any digit from 0-9
10 – base
𝑒 – exponent, the number of times the decimal point is moved to either
towards left or right
Scientific Notation

3. Sir Melo
.
Scientific Notation
Rules in expressing standard notation to scientific notation:
1.When the decimal point is moved from right to left, the result
is positive exponent.
Example: 7806. 123 = 7. 806123 × 103
= 7.81 × 103
2.When the decimal point is moved left to right, the result is
negative exponent.
Example: 0.00007806123 = 7.806123 × 10−5 = 7.81 × 10−5

4. Sir Melo
.
Scientific Notation
Rules converting scientific notation back to standard notation are shown below.
Move the current decimal point according to the number of places based on the
exponent
(+) positive exponent : move to the RIGHT
Example:
(−) negative exponent : move to the LEFT
Example:

5. Sir Melo
Rules in Addition and Subtraction involving scientific notation
When two or more quantities are added or subtracted, make sure the exponents are the same.
𝐼𝑓 𝑛𝑜𝑡, 𝑐ℎ𝑜𝑜𝑠𝑒 𝑜𝑛𝑒 𝑡𝑜 𝑎𝑑𝑗𝑢𝑠𝑡 𝑡ℎ𝑒 𝑑𝑒𝑐𝑖𝑚𝑎𝑙 𝑎𝑛𝑑 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡. 𝑈𝑠𝑒 𝐿𝐴𝑅𝑆 (𝐿𝑒𝑓𝑡 𝐴𝑑𝑑, 𝑅𝑖𝑔ℎ𝑡 𝑆𝑢𝑏𝑡𝑟𝑎𝑐𝑡)
Add/subtract the number. Keep the exponent the same.
Example:
6.2 × 103
+ 1.74 × 103
= 6.2 + 1.74 × 103
= 7.94 × 103
7.1 × 103
+ 5.2 × 105
= 0.071 × 105
+ 5.2 × 105
= 5.271 × 105
- 𝐿𝑒𝑓𝑡 𝐴𝑑𝑑, 𝑅𝑖𝑔ℎ𝑡 𝑆𝑢𝑏𝑡𝑟𝑎𝑐𝑡 𝑜𝑟 𝐿𝐴𝑅𝑆 (here we will adjust 7.1 × 103
to have an exponent of 105
)
-From 103
𝑡𝑜 105
, we will move two decimal places to the left since we added two to the exponent, that
becomes 0.071 × 105
Scientific Notation

6. Sir Melo
Unit Consistency and Conversion of Units
There are two major systems of units in the world namely; SI (derived
from French Systeme International) units also known as Metric
system and the English system. Although the system of units used by
engineers and scientists is the metric system since 1960, some
countries continue to adapt the English system of units like for
example the United States of America. However, the conversions
between the SI unit and English system of units have been well-
defined.

7. Sir Melo
Multiplying and/or dividing units just like ordinary algebraic expressions give an easy way to
convert a quantity from one unit to another to be dimensionally consistent.
Example:
To convert 0.58 𝑚 to 𝑚𝑚
Conversion factor to be used: 1𝑚 = 1 000 𝑚𝑚
0.28 𝑚 ×
1000 𝑚𝑚
1 𝑚
= 280 𝑚𝑚
To convert 90 𝑘𝑚/ℎ in meters per second
Conversion factors to be used:
1𝑘𝑚 = 1, 000 𝑚 1 ℎ𝑟 = 60 𝑚𝑖𝑛 1 𝑚𝑖𝑛 = 60 𝑠
Unit Consistency and Conversion of Units

8. Sir Melo
90
𝑘𝑚
ℎ
×
1000 𝑚
1 𝑘𝑚
×
1 ℎ
60 𝑚𝑖𝑛
×
1 𝑚𝑖𝑛
60 𝑠
= 25 𝑚
𝑠
Answer: o convert 50
𝑘𝑔
𝑚3 to
𝑔
𝑐𝑚3

9. Sir Melo
Unit Consistency and Conversion of Units
To convert 50
𝑘𝑔
𝑚3 to
𝑔
𝑐𝑚3
Conversion factors to be used:
1 𝑘𝑔 = 1000 𝑔 1 𝑚 = 100 𝑐𝑚
50
𝑘𝑔
𝑚3
×
1000 𝑔
1 𝑘𝑔
×
1𝑚
100 𝑐𝑚
3
= 0.05
𝑔
𝑐𝑚3

10. Sir Melo
Unit Consistency and Conversion of Units
Converting units with different prefixes
Example: convert 5 Megameter to meter
5 𝑀𝑚 → 𝑚𝑒𝑔𝑎 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑡𝑎𝑏𝑙𝑒 𝑎𝑏𝑜𝑣𝑒 𝑚𝑒𝑎𝑛𝑠 106
5 𝑀𝑚 = 5 × 106
𝑚

11. Sir Melo
Unit Consistency and Conversion of Units
Example: convert 7 𝑚𝑖𝑙𝑙𝑖𝑔𝑟𝑎𝑚𝑠 to 𝑔𝑟𝑎𝑚𝑠
7 𝑚𝑔 → 𝑚𝑖𝑙𝑙𝑖 𝑚𝑒𝑎𝑛𝑠 10−3𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑡𝑎𝑏𝑙𝑒
7 𝑚𝑔=7 × 10−3𝑔
Example: 5 𝑘𝑚 to 𝑐𝑚
kilo means 103 so, 5 𝑘𝑚 = 5 × 103𝑚
1 𝑐𝑚 = 1 × 10−2 𝑚
5 × 103
𝑚 ×
1 𝑐𝑚
1×10−2 𝑚
= 5 × 105
𝑐𝑚 𝑜𝑟 500, 000 𝑐𝑚

12. Sir Melo
Unit Consistency and Conversion of Units
* ANOTHER way to do this: 5 𝑘𝑚 to 𝑐𝑚
Step 1: subtract exponents
*kilo has exponent of 103
and centi has exponent of 10−2
from kilo to centi
3 subtract -2 = 5

13. Sir Melo
Unit Consistency and Conversion of Units
Step 2: move decimal places according to difference of exponents to the direction of wanted
unit.
* move the decimal 5 places to the right (toward centi)
5 𝑘𝑚 = 5 0 0 0 0 0 𝑐𝑚 or 5 × 105
𝑐𝑚
5 decimal places to the right

14. Sir Melo
Unit Consistency and Conversion of Units
Example: 384.0 𝑚𝑔 to 𝑑𝑔
milli means 10−3
so, 384.0 𝑚𝑔 = 384.0 × 10−3
𝑔
conversion factor 1𝑑𝑔 = 0.1 𝑔
384.0 × 10−3
𝑔 ×
1 𝑑𝑔
0.1 𝑔
= 3. 840 𝑑𝑔

15. Sir Melo
Unit Consistency and Conversion of Units
* ANOTHER way to do this: 384.0 𝑚𝑔 to 𝑑𝑔
Step 1: subtract exponents
*milli has exponent of 10−3
and deci has exponent of 10−1
-1 − -3 = 2
deci milli

16. Sir Melo
Unit Consistency and Conversion of Units
Step 2: move decimal places according to difference of exponents to the direction of wanted
unit.
* move the decimal 2 places to the left (toward deci)
384.0 𝑚𝑔 = 3. 8 4 0 𝑑𝑔
2 decimal places to the left