1. SI CONVERSIONS:
Suppose you are planning a pizza party. Each person will get one slice. How many pizzas are needed for 32 students (32 slices)?
Pizza and slices cannot be compared because they are different units.
But if each pizza has been divided into 8 slices, then
1 pizza = 8 slices.
This can be rewritten in the following ways:
𝟏 𝒑𝒊𝒛𝒛𝒂 𝟖 𝒔𝒍𝒊𝒄𝒆𝒔 or 𝟖 𝒔𝒍𝒊𝒄𝒆𝒔 𝟏 𝒑𝒊𝒛𝒛𝒂
(Conversion Factors)

2. SI CONVERSIONS:
You must multiply the number of slices (32) by the proper conversion factor.
The conversion factor should be the one that has in the denominator the same unit than the original value :
32 slices x
𝟏 𝒑𝒊𝒛𝒛𝒂 𝟖 𝒔𝒍𝒊𝒄𝒆𝒔
= 4 pizzas

3. Multiply when converting from larger to smaller units.
Practice:
1) How many millimeters are in 4 m?
Determine the possible conversion factors:
The two units in this problem are m and mm, if
1 m = 1,000 mm, then
4 m x or
Multiply when converting from larger to smaller units.
= 4 x 103 mm
(4,000 mm)

4. Divide when converting from smaller to larger units.
Practice:
2) How many meters are in 54 cm?
Determine the conversion factors:
The two units in this problem are m and cm, &
1 m = 100 cm, then
54 cm x or
Divide when converting from smaller to larger units.
= 0.54 m

5. Giga (G) ---------- 109 base units Mega (M) --------- 106 base units
Kilo (k) base units
Hecto (h) base units
Deca (da) base units
BASE UNIT (m, L, g,…..)
Deci (d) base units
Centi (c) base units
Milli (m) base units
Micro (μ) base units
Nano (n) base units
Pico (p) base units

6. Measurement and SI Units:
Meter (m) for length
Liter (L) for volume
Gram (g) for mass
Base units
Second (s) for time
Kelvin (K) for temperature
Joule (J) for energy

7. Multiply when converting from larger to smaller units.
Practice:
3) How many decaliters are in 3 kiloliters?
Determine the possible conversion factors:
The two units in this problem are daL and kL.
1 kL = 102 daL (because = 102 ).
3 kL x or
Multiply when converting from larger to smaller units.
= 3 x 102 daL
( 300 daL)

8. Multiply when converting from larger to smaller units.
Practice:
4) How many nanograms are in 25 decigrams?
Determine the possible conversion factors:
The two units in this problem are ng and dg.
1 dg = 108 ng (because 10-1-(-9) = ).
25 dg x or
Multiply when converting from larger to smaller units.
= 2.5 x 109 ng

9. Exercises (show your work) (notebooks):
I - Convert:
5.00 Km = __________ cm.
2) 250 mL = ___________ nL.
3) 8 kg = ______________ Gg.
4) 1,000 mg = __________ kg.

10. Exercises (show your work) (notebooks):
I - Convert:
5.00 Km = __________ cm.
5.00 x 105
Kilo – to - centi ----
103 – (-2) =
105
1 Km = 105cm
5.00 Km x 𝟏𝟎𝟓 𝒄𝒎 𝟏 𝑲𝒎 =
5.00 x 105cm
(5,000 cm)

11. Exercises (show your work) (notebooks):
I - Convert:
2) 200 mL = __________ nL.
2 x 108
milli – to - nano ----
10-3 – (-9) =
106
1 mL = 106nL
200 mL x 𝟏𝟎𝟔 𝒏𝑳 𝟏 𝒎𝑳 =
2 x 108 nL
(200,000,000 nL)

12. Exercises (show your work) (notebooks):
I - Convert:
3) 8 Kg = __________ Gg.
8 x 10-6
Kilo – to - giga ----
103 – 9 =
10-6
1 Kg = 10-6 Gg
8 Kg x 10−6𝑮𝒈 𝟏 𝑲𝒈 =
8 x 10-6 Gg
(0.000,008 Gg)

13. Exercises (show your work) (notebooks):
I - Convert:
4) 1,000 mg = __________ Kg.
1 x 10-3
milli – to - kilo ----
10-3 – 3 =
10-6
1 mg = 10-6 Kg
1,000 mg x 10−6𝑲𝒈 𝟏 𝒎𝒈 =
1 x 10-3 Kg
(0.001 Kg)

14. Multiply Divide Giga (G) ---- 109 Mega (M) --- 106 Kilo (K) ----- 103
Hecto (h)
Deca (da)
BASE UNIT
Deci (d)
Centi (c)
Milli (m)
Micro (μ)
Nano (n)
Pico (p)
Shift the decimal point to the left
Shift the decimal point to the right
Divide

15. Exercises (show your work) (notebooks):
II - Convert:
12 hm = ________ cm.
2) 20 L = _________ mL.
3) 400 kg = _________ Gg.
4) 1,000 dg = _______ hg.

16. Exercises (show your work) (notebooks):
II - Convert:
12 hm = ________ cm.
Giga (G)
Mega (M)
Kilo (K)
Hecto (h)
Deca (da)
BASE UNIT
Deci (d)
Centi (c)
Milli (m)
Micro (μ)
Nano (n)
Pico (p)
120,000
4 places
(going down)
Shift the decimal point to the right:
12 hm = 12
12 hm =
120,000 cm

17. Exercises (show your work) (notebooks):
II - Convert:
2) 20 L = ________ mL.
Giga (G)
Mega (M)
Kilo (K)
Hecto (h)
Deca (da)
BASE UNIT
Deci (d)
Centi (c)
Milli (m)
Micro (μ)
Nano (n)
Pico (p)
20,000
3 places
(going down)
Shift the decimal point to the right:
20 L = 20
20 L =
20,000 mL

18. Exercises (show your work) (notebooks):
II - Convert:
3) 400 kg = ________ Gg.
Giga (G)
Mega (M)
Kilo (K)
Hecto (h)
Deca (da)
BASE UNIT
Deci (d)
Centi (c)
Milli (m)
Micro (μ)
Nano (n)
Pico (p)
6 places
(going up)
Shift the decimal point to the left:
400 kg = .
400
400 kg = Gg

19. Exercises (show your work) (notebooks):
II - Convert:
4) 1,000 dg = ________ hg.
Giga (G)
Mega (M)
Kilo (K)
Hecto (h)
Deca (da)
BASE UNIT
Deci (d)
Centi (c)
Milli (m)
Micro (μ)
Nano (n)
Pico (p) 1
3 places
(going up)
Shift the decimal point to the left:
1,000 dg =
1 000 .
1,000 dg =
1 hg

20. Derived units are “built” from SI units:
cm2, m2
Ex.
How can you calculate de area of the football field?
How can you calculate de volume of this classroom?
How can you calculate de density of ?
area
m3 ; cm3
volume
g/cm3
density

21. Converting Units: 1 cm = 101 mm 1 cm3 = 101x3 mm3 = 103 mm3
1 cm = 101 mm
1 cm3 = 101x3 mm3
= 103 mm3
(1,000 mm3)
1 cm2 = mm2
101x2
= 102 mm2
(100 mm2)
1 m = 103 mm
1 m3 = mm3
103x3
= 109 mm3
(1,000,000,000 mm2)

22. Exercises (show your work) (notebooks):
III - Convert:
12 cm2 = ________ mm2
2) 15 m2 = _________ cm2
3) 10 dm3 = ________ cm3
4) 1 m3 = __________ mm3

23. So, units must be the same before adding or
Arithmetic with units:
In addition or subtraction the units should be
the same: kg + 3 kg = 5 kg m - 12 m = 400 m
So, units must be the same before adding or
subtracting!
3.001 kg g =
3.001 kg kg
= kg
4.314 Gm - 2 Mm =
4.314 Gm Gm
= Gm

24. Arithmetic with units:
In multiplication or division: the units must be multiplied or divided too: m × 3 m =
Sometime, units may cancel: g / 10 g =
9 m2
10 kg x 9.8 m/s2 =
98 kg m/s2
0.5
(no units)
10.00 m/s x in/m =
393.7 in/s

25. Exercises (show your work) (notebooks):
IV - Solve:
12 cm cm2 =
2 m – 10 cm =
3) 2 cm x 3 cm x 6 cm =
3) 25 kg ÷ 5 kg =
4) 45 km ÷ 0.5 h =

26. K = oC + 273 oC = K - 273 Temperature in SI units:
The difference between the two scales (Celsius, °C & Kelvin, K) is their zero point:
- The zero point in Celsius is the freezing point of water.
- The zero point on the Kelvin scale is absolute zero.
00 K = - 273°C.
(Absolute zero (zero K) is the coldest temperature
theoretically possible).
You can convert between Kelvin and Celsius by using either of the following equations:
K = oC
oC = K

27. Temperature in SI units: Example: Express 25°C in kelvins.
K = oC
K =
= K
Temperature in Fahrenheit:
F = 1.8 x oC
oC =

28. Exercises (show your work) (notebooks):
IV - Convert:
25oC = __________ K.
273 K = _________ oC
3) 25oC = __________ K.
3) 300 K = _________ oC