SI units and Sig. Figs. measurement

SI (système internationale) Physical Quantity Unit Symbol Volume Cubic Metre (litre) m3 Length Metre m Mass Kilogram kg Time Second s Temperature Kelvin K Amount of substance Mole mol Electric current Ampere A Luminous intensity Candela cd

Scientific Notation Scientists have developed a shorter method to express very large numbers. Scientific Notation is based on powers of the base number 10.

Scientific notation 123,000,000,000 in s.n. is 1.23 x 1011 The first number 1.23 is called the coefficient. It must be between 1 - 9.99 The second number is called the base . The base number 10 is always written in exponent form. In the number 1.23 x 1011 the number 11 is referred to as the exponent or power of ten. This large number only has 3 significant digits

To write a large number in scientific notation: ex: 36 000 First put the decimal after the first digit and drop the zeroes. Ex: 3.6 Next, count the number of places from the decimal to the end of the number. Ex: 4 Finally, put it together. Ex: 3.6 x 104 36 000 only has two significant digits

To write a small number in s.n. ex: 0.03064 First move the decimal after the first real number and drop the zeroes. Ex: 3.064 Next, count the number of places moved from the original decimal spot to the new decimal spot. Ex: 2 Numbers less than 1 will have a negative exponent. Ex: -2 Finally, put it together. Ex: 3.064 x 10-2 0.03064 has four significant digits

Precision: to describe how well a group of measurements made of the same object or event under the same conditions actually do agree with one another. These points are precise with one another but not accurate.

Accuracy: represents the closeness of a measurement to the true value. Ex: the bulls-eye would be the true value, so these points are accurate.

Why Significant Figures? When we take measurements or make calculations, we do so with a certain precision. This precision is determined by the instrument we use to take those measurements. So, when we do calculations based on our measurements, the calculations must be only as precise as the measurements.

Using sig figs: The Rules! 487 All significant Digits from 1-9 are always significant. Zeros between two other significant digits are always significant One or more additional zeros to the right of both the decimal place and another significant digit are significant. Zeros used solely for spacing the decimal point (placeholders) are not significant. 2002 All significant 6.00 All significant 47 000 Only two significant digits

EXAMPLES # OF SIG. DIG. COMMENT 453kg 3 All non-zero digits are always significant. 5057L 4 Zeros between 2 sig. dig. are significant. 5.00 Additional zeros to the right of decimal and a sig. dig. are significant. 0.007 1 Placeholders are not sig.

Problems: Indicate the number of significant figures... 1. 1.235 ______ 2. 2.90 ______ 3. 0.0987 ______ 4. 0.450 ______ 5. 5.00 ______ 6. 2300 ______ 7. 230 ______ 8. 230.0 ______ 9. 9870345 ______ 10. 1.00000 ______

Multiplying and Dividing RULE: your answer may only show as many sig figs as the multiplied or divided measurement showing the least number of significant digits. Example: 22.37 cm x 3.10 cm = 69.3 only 3 sig figs allowed.

Multiplying and Dividing Practice 1. 42.3 x 2.61 ______ 2. 32.99 x 0.23 ______ 3. 46.1 ÷ 1.21 ______ 4. 23.3 ÷ 4.1 ______ 5. 0.61 x 42.1 ______ 6. 47.2 x 0.02 ______ 7. 47.2 ÷ 0.023 ______ 8. 100 x 23 ______ 9. 120 ÷ 0.12 ______ 10. 120 x 12 ÷ 12.5 ______

Adding and Subtracting: RULE: your answer can only show as many decimal places as the measurement having the fewest number of decimal places. Example: 3.76 g + 14.83 g + 2.1 g = 20.7 g

Adding and Subtracting Practice 1. 2.634 + 0.02 ______ 2. 2.634 - 0.02 ______ 3. 230 + 50.0 ______ 4. 0.034 + 1.00 ______ 5. 4.56 - 0.34 ______ 6. 3.09 - 2.0 ______ 7. 349 + 34.09 ______ 8. 234 - 0.98 ______ 9. 238 + 0.98 ______ 10. 123.98 + 0.54 - 2.3 ______