THE METRIC SYSTEM AND SIG FIGS
Metric System
The system of measurements that is used by scientists around the world is a revised metric system called
the International System of Units (abbreviated SI). The SI units are the following:
Tetra(𝟏𝟏 ) Giga(𝟏𝟏 ) Mega(𝟏𝟏 ) kilo(𝟏𝟏
𝟏𝟏
𝟏
𝟏
𝟏
)
Hecta(𝟏𝟏𝟏) Deca(𝟏𝟏𝟏)
[base unit]-meter, gram, liter, second (100)
deci(𝟏𝟏−𝟏) centi(𝟏𝟏−𝟏) milli(10−3) μmicro(10−6) nano(10−9) pico(10−12)
*1 cm3 = 1 mL
To convert from…
ºCelsius → ºFahrenheit : ºF = 9/5 ºC + 32
ºFahrenheit→ ºCelsius : ºC = 5/9 ºF - 32
To measure temperature on the Kelvin scale…
K = ºC + 273
Significant Figures
Counting Sig Figs
Any digit that is not zero is considered a significant number, but zeros that are in between
nonzero digits are significant:
12.34 cm has 4 sig figs
103 mL has 3 sig figs
The general rule for counting sig figs is to count from the left to the right when there is no
decimal point in the number, and from right to left when there is a decimal point in the number,
and disregarding the trail of zeros:
3.0670 mg has 5 sig figs
0.000080 mm has 2 sig figs
340000000 L has 2 sig figs*
*can be changed by using scientific
notation: 3.40e8 has 3 sig figs
Sig Figs in Calculations
When adding or subtracting, the number of decimal places in the answer cannot be more than
the number of decimal places in any of the original numbers:
3.985
+ 1.5 _
_____________5.485 ⇒round to 5.5
When multiplying or dividing, the number of significant figures in the final answer is
determined by the original number with the smallest number of significant figures:
8.394
x 2.4 _
_____________20.1456 ⇒round to 20
PRACTICE PROBLEMS:
Metric System:
6) 87 cm3 = _____ L
7) 89ºC = _____ Kelvins
8) 762.45 kL = _____ dL
9) 98ºF = _____ Kelvins
10) 987 Tg = _____ mg
1) 100 Hg = ________ dg
2) 37ºC = _____ ºF
3)10 mL = _______ ML
4) 743 μm = ______m
5) 110ºF= _____ºC
Significant Figures:
Determine the number of sig figs
1) 83.0921
2) 9.000030
3) 340000
4) 77.0
5) 0.02
6) 3045.0
Add/Subtract:
1) 548.1+0.001
2) 865+9.45+0.4
3) 340000+4.2
4) 862.30-111.1
5) 754.0-0.258
6) 0.006-0.0005
Multiply/Divide:
1 ) 2.56x0.06
4) 560/3.49
2) 0.45x5
3) 300040x0.2
5) 1443/11.1
6) 12.00/5.6
PRACTICE PROBLEMS ANSWER KEY:
Metric System:
6) 87 cm3 = 0.087 L
7) 89ºC = 362 Kelvins
8) 760.55 kL = 760550 dL
9) 98ºF = 22.4 Kelvins
10) 987 Tg = 0.987 ∗ 10−3 Mg
1) 100 Hg = 0.1 dg
2) 37ºC = 98.6 ºF
3)10 mL = 10 ∗ 10−10 ML
4) 743 μm = 0.743−3 m
5) 110ºF= 29.1ºC
Significant Figures:
Determine the number of sig figs
1) 83.0921
2) 9.000030
3) 340000
6
7
2
4) 77.0
3
5) 0.02
2
6) 3045.0 5
Add/Subtract:
1) 548.1+0.001
548.1
2) 865+9.45+0.4 875
3) 340000+4.2 340004
4) 862.30-111.1
5) 754.0-0.258
6) 0.006-0.0005
Multiply/Divide:
1 ) 2.56x0.06
2) 0.45x5
3) 300040x0.2
0.2
2
60000
4) 560/3.490
160
5) 1443/11.1
6) 12.001/5.612
130.
2.138
751.2
753.7
0.006