Introduction to analysis

Data handling, errors and so on

Common Decimal Prefixes Used with SI Units.

Prefix Prefix Number Word Exponential Symbol Notation

tera T 1,000,000,000,000 trillion 1012

giga G 1,000,000,000 billion 109

mega M 1,000,000 million 106

kilo k 1,000 thousand 103

hecto h 100 hundred 102

deka da 10 ten 101

----- ---- 1 one 100

deci d 0.1 tenth 10-1

centi c 0.01 hundredth 10-2

milli m 0.001 thousandth 10-3

micro millionth 10-6

nano n 0.000000001 billionth 10-9

pico p 0.000000000001 trillionth 10-12

femto f 0.000000000000001 quadrillionth 10-15

Rules for Determining Which Digits are Significant

All digits are significant, except zeros that are used only toposition the decimal point.

1. Make sure that the measured quantity has a decimal point.2. Start at the left of the number and move right until you reach the first nonzero digit.3. Count that digit and every digit to its right as significant.Zeros that end a number and lie either after or before the decimal point are significant; thus 1.030 ml has four significant figures, and 5300. L has four significant figures also. Numbers such as 5300 L is assumed to only have 2 significant figures. A terminal decimal point is occasionally used to clarify the situation, but scientific notation is the best!

Examples of Significant Digits in Numbers

Number - Sig digits Number - Sig digits

0.0050 two18.00 four0.0012 two83.001 five875,000 three30,000 one5.0000 five

23,001.00 seven

0.000108 three

1,470,000 three

1.3400 X 107 five5600 two87,000 two

78,002.3 six

0.00007800 four

1.089 X 10-6 four0.0000003 one1.00800 six1,000,000 one

Rules for Significant Figures in Answers

1. For multiplication and division. The number with the least certainty limits the certainty of the result.

Therefore, the answer contains the same number of significant figures as there are in the measurement with the fewest significant figures.

Multiply the following numbers: 9.2 cm x 6.8 cm x 0.3744 cm = 23.4225 cm3 = 23 cm3

2. For addition and subtraction. The answer has the same number of decimal places as there are in the measurement with the fewest decimal places. Add the following volumes: 83.5 ml + 23.28 ml = 106.78 ml = 106.8 mlExample subtracting two volumes: 865.9 ml - 2.8121393 ml = 863.0878607 ml = 863.1 ml

Rules for Rounding Off Numbers:1. If the digit removed is 5 or more, the preceding number increases by 1 : 5.379 rounds to 5.38 if three significant figures are retained and to 5.4 if two significant figures are retained.

2. If the digit removed is less than 5, the preceding number is unchanged : 0.2413 rounds to 0.241 if three significant figures are retained and to 0.24 if two significant figures are retained.

3. Be sure to carry two or more additional significant figures through a multistep calculation and round off only the final answer.

Precision and Accuracy Errors in Scientific Measurements

Precision - Refers to reproducibility or How close the measurements are to each other.

Accuracy - Refers to how close a measurement is to the real value.

Systematic error - produces values that are either all higher or all lower than the actual value.

Random Error - in the absence of systematic error, produces some values that are higher and some that are lower than the actual value.

Constant errors

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Proportional errors

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Constant & Proportional Errors