CONVERSION OF UNITS

Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

Metric prefixes in everyday use

Text	Symbol	Factor
tera	T	1000000000000
giga	G	1000000000
mega	M	1000000
kilo	k	1000
hecto	h	100
deca	da	10
(none)	(none)	1
deci	d	0.1
centi	c	0.01
milli	m	0.001
micro	μ	0.000001
nano	n	0.000000001
pico	p	0.000000000001

The factor-label method is the sequential application of conversion factors expressed as fractions and arranged so that any dimensional unit appearing in both the numerator and denominator of any of the fractions can be cancelled out until only the desired set of dimensional units is obtained. For example, 10 miles per hour can be converted to meters per second by using a sequence of conversion factors as shown below:

Exercises:

1.) 18 mm to m

2.) 400.0 nm to m

3.) 0.000000000154 m to mm

4.) 0.43 L to dL

5.) 1.43 kg/L to g/mL

Answers:

1.

2.

 3.

 

4. 

 

5.

  

SIGNIFICANT FIGURES

The significant figures of a number are those digits that carry meaning contributing to its precision.

Specifically, the rules for identifying significant figures when writing or interpreting numbers are as follows:

• All non-zero digits are considered significant. For example, 91 has two significant figures (9 and 1), while 123.45 has five significant figures (1, 2, 3, 4 and 5).
• Zeros appearing anywhere between two non-zero digits are significant. Example: 101.1203 has seven significant figures: 1, 0, 1, 1, 2, 0 and 3.
• Leading zeros are not significant. For example, 0.00052 has two significant figures: 5 and 2.
• Trailing zeros in a number containing a decimal point are significant. For example, 12.2300 has six significant figures: 1, 2, 2, 3, 0 and 0. The number 0.000122300 still has only six significant figures (the zeros before the 1 are not significant). In addition, 120.00 has five significant figures since it has three trailing zeros. This convention clarifies the precision of such numbers; for example, if a measurement precise to four decimal places (0.0001) is given as 12.23 then it might be understood that only two decimal places of precision are available. Stating the result as 12.2300 makes clear that it is precise to four decimal places (in this case, six significant figures).
• The significance of trailing zeros in a number not containing a decimal point can be ambiguous. For example, it may not always be clear if a number like 1300 is precise to the nearest unit (and just happens coincidentally to be an exact multiple of a hundred) or if it is only shown to the nearest hundred due to rounding or uncertainty. 

Determine the number of significant figures in each of the following:
 

a) 3427	b) 0.00456	c) 123,453
d) 172	e) 0.000984	f) 0.502
g) 3.01 x 102	h) 1.14 x 104	i) 107.2
j) 0.0000455
		Answers: 4, 3, 6, 3, 3, 3, 3, 3, 4, 3

SCIENTIFIC NOTATION

 Scientific notation (commonly referred to as "standard form" or "standard index form") is a way of writing numbers that are too big or too small to be conveniently written in decimal form. Scientific notation has a number of useful properties and is commonly used in calculators and by scientists, mathematicians and engineers.

Standard decimal notation	Normalized scientific notation
2	2×100
300	3×102
4,321.768	4.321768×103
−53,000	−5.3×104
6,720,000,000	6.72×109
0.2	2×10−1
0.000 000 007 51	7.51×10−9

In this practice, you will be converting numbers to and from scientific notation. 

 A. Express in correct scientific notation:

1.) 61,500

2.) 0.0000568

3.) 321

4.) 64,960,000

5.) 0.070850

B. Express in correct standard form:

6.) 1.09 x 10³

7.) 4.22715 x 10⁸ 

8.) 3.078 x 10^-4 

9.)9.004 x 10^-2  
10.) 5.1874 x 10² 

^Answers: 

^{1.  6.15 E 4}

^{2. 5.68 E -5}

^{3. 3.21 E 2}

^{4. 6.496 E 7}

^{5. 7.0850 E -2}

^{6. 1,090}

^{7. 422,715,000}

^{8. 0.0003078}

^{9. 0.09004}

^{10. 518.74}

     

^{source : http://en.wikipedia.org/wiki/Scientific_notation}

UNCERTAINTY OF MEASUREMENT

 

         
    Uncertainty of measurement is the doubt that exists about the result of any measurement. You might think that well-made rulers, clocks and thermometers should be trustworthy, and give the right answers. But for every measurement - even the most careful - there is always a margin of doubt. In everyday speech, this might be expressed as ‘give or take’ ... e.g. a stick might be two meters long 'give or take a centimeter'.



Take a look at the difference in measurement readings using these two different rulers.

Using the ruler below, how long is this leaf?


(measurement in centimeters)






Answer: about 3.56 cm

source: https://www.wmo.int/pages/prog/gcos/documents/gruanmanuals/UK_NPL/mgpg11.pdf