Ch 5 Ch 5 MeasurementsMeasurements

Scientific measurements are based Scientific measurements are based on the metric system. This is a on the metric system. This is a decimal based system that uses a decimal based system that uses a system of prefixes to relate the system of prefixes to relate the magnitude of the quantity. It is magnitude of the quantity. It is essential that you are able to work essential that you are able to work fluently in the metric system.fluently in the metric system.

Metric QuantitiesMetric Quantities

The standard unit of length is the The standard unit of length is the metermeter (m) (m) The standard measure of mass is the The standard measure of mass is the gramgram

(g)(g) The standard unit of Temperature is The standard unit of Temperature is CelsiusCelsius

(C) or (C) or KelvinKelvin (K) T (K) Tkk = T = Tcc + 273.15 + 273.15 The standard unit of volume is either:The standard unit of volume is either:

Cubic centimeters (cc) 1 m = 1,000,000 cmCubic centimeters (cc) 1 m = 1,000,000 cm33

Liters (L) 1 L = 1000 mLLiters (L) 1 L = 1000 mL Milliliters (mL) 1 mL = 1 ccMilliliters (mL) 1 mL = 1 cc

Converting metric/metricConverting metric/metricConverting metric/englishConverting metric/english

Q How many decimal places do I move How many decimal places do I move it??it??

A Please do not ask this question or use Please do not ask this question or use this technique. We will use a system this technique. We will use a system of conversion called dimensional of conversion called dimensional analysis. It converts values using analysis. It converts values using factors of one that have both the factors of one that have both the known and unknown quantities in known and unknown quantities in them. We will use the same technique them. We will use the same technique for m/m and m/e conversions.for m/m and m/e conversions.

Conversion FactorsConversion Factors

A conversion factor is a ratio of one that A conversion factor is a ratio of one that includes the known and unknown includes the known and unknown quantities.quantities.

First find an equality between the known First find an equality between the known and unknown. 1.609 km = 1.0 miand unknown. 1.609 km = 1.0 mi

Turn it into a ratio with the unknown Turn it into a ratio with the unknown desired quantity in the numerator desired quantity in the numerator 1.609 1.609 kmkm

Multiply the ratio by the known valueMultiply the ratio by the known value

1.0 mi

Example #1Example #1 Convert a 10.0 km race to milesConvert a 10.0 km race to miles Known quantity is 10.0 milesKnown quantity is 10.0 miles Known equality is 1.609 km = 1.0 Known equality is 1.609 km = 1.0

milesmiles The ratio used is The ratio used is 1.0 mi1.0 mi

Use initial quantity x conversion Use initial quantity x conversion factor = answerfactor = answer

10.0 km x 10.0 km x 1.0 mi1.0 mi = 6.22 mi = 6.22 mi

1.609 km

1.609 km

Rounding Off & Significant Rounding Off & Significant FiguresFigures

It is important to be honest when It is important to be honest when reporting a measurement, so that it does reporting a measurement, so that it does not appear to be more accurate than the not appear to be more accurate than the equipment used to make the measurement equipment used to make the measurement allows. We can achieve this by controlling allows. We can achieve this by controlling the number of digits, or the number of digits, or significant significant figuresfigures, used to report the measurement. , used to report the measurement.

Use the rules of significant figures Use the rules of significant figures whenever you are reporting a calculated whenever you are reporting a calculated value derived from collected or given datavalue derived from collected or given data

Rules for Significant Rules for Significant FiguresFigures Non-zero integers are always significant. The Non-zero integers are always significant. The

number 23.43 has four significant figuresnumber 23.43 has four significant figures Zeros Zeros withinwithin a number are always significant. Both a number are always significant. Both

4308 and 40.05 contain four significant figures. 4308 and 40.05 contain four significant figures. Zeros that do nothing but set the decimal point Zeros that do nothing but set the decimal point

are not significant. Thus, 470,000 has two are not significant. Thus, 470,000 has two significant figures. significant figures.

Trailing zeros that aren't needed to hold the Trailing zeros that aren't needed to hold the decimal point are significant. Thus, 4.00 has three decimal point are significant. Thus, 4.00 has three significant figures. significant figures.

Zeros prior to a number less than 1 are not Zeros prior to a number less than 1 are not significant. Thus, 0.000203 has 3 significant significant. Thus, 0.000203 has 3 significant figures figures

How many significant How many significant figures?figures?

15.0215.02 fourfour 15.015.0 threethree 0.015020.01502 fourfour 100100 oneone

276.2276.2 fourfour 400.0400.0 fourfour 8.98.9 twotwo 40024002 fourfour

Rules for CalculatingRules for Calculating Add/SubtractAdd/Subtract

• Round the Round the answer to answer to the least the least significant significant decimal decimal placeplace

Multiply/DivideMultiply/Divide• Round your Round your

answer to the answer to the number of number of significant significant figures figures contained in contained in the least the least precise precise numbernumber

Example #2Example #2

Calculate 1.302 + 0.26 =Calculate 1.302 + 0.26 = Answer = 1.56Answer = 1.56 Calculate 6,020 – 17.36 =Calculate 6,020 – 17.36 = Answer = 6000Answer = 6000 Calculate 9.81 * 75 =Calculate 9.81 * 75 = Answer = 740Answer = 740 Calculate 6.022 Calculate 6.022 0.0405 = 0.0405 = Answer = 149Answer = 149