MeasurementsMeasurements

What do we measure? What do we measure?

Fundamental properties Fundamental properties mass (weight)mass (weight) kkilogram ilogram lengthlength mmeter eter timetime ssecond econd temperaturetemperature KelvinKelvin

Derived quantities Derived quantities density, velocity, force, etc...density, velocity, force, etc...

Using the metric systemUsing the metric system In the metric system, prefixes are used In the metric system, prefixes are used

to identify the multiples of ten. to identify the multiples of ten. 101033 10 1022 10 1011 1 10 1 10-1-1 10 10-2-2 10 10-3-3 Kilo Hecto Deka BASE Deci Centi Milli Kilo Hecto Deka BASE Deci Centi Milli

Base unitsBase units mass mass gram(g) gram(g) length length meter (m) meter (m) liquid volume liquid volume liter (l) liter (l) time time second (s)second (s)

Each multiple is one decimal place. Each multiple is one decimal place.

Move the decimal to convert Move the decimal to convert

Moving the decimal Moving the decimal For measurements that are defined by a For measurements that are defined by a

single unit such as length, mass, or liquid single unit such as length, mass, or liquid volume , etc., simply move the decimal the volume , etc., simply move the decimal the number of places indicated by the prefix. number of places indicated by the prefix.

400 m = 40,000 cm400 m = 40,000 cm

75 mg = 0.075 g75 mg = 0.075 g

For area measurements, they are the For area measurements, they are the combination of two dimensions, you move combination of two dimensions, you move

the decimal twice the number of places.the decimal twice the number of places. 2.5 m2.5 m22 = 2,500,000 mm = 2,500,000 mm22

Converting measurements Converting measurements

Metric Metric Metric Metric multiples of 10 multiples of 10 move decimal or use conversions move decimal or use conversions

EnglishEnglish Metric Metric conversion factors conversion factors unit cancellation methodunit cancellation method

Converting MetricConverting Metric English English

When converting in the US (English) system or When converting in the US (English) system or converting between US and metric units it is converting between US and metric units it is necessary to use proportions. necessary to use proportions.

In the example below, the measurement 12 in. In the example below, the measurement 12 in. is converted to cm. The conversion factor 1 in is converted to cm. The conversion factor 1 in = 2.54cm is written as a ratio. = 2.54cm is written as a ratio.

12 in. x 12 in. x 2.54 cm2.54 cm = 30.48 cm = 30.48 cm 1 in.1 in.

PracticePractice

A rattlesnake is 2.44 m long. How A rattlesnake is 2.44 m long. How long is the snake in cm?long is the snake in cm?

1) 1) 2440 cm2440 cm

2)2) 244 cm244 cm

3)3) 24.4 cm24.4 cm

SolutionSolution

A A rattlesnake is 2.44 m long. How long is the rattlesnake is 2.44 m long. How long is the snake in cm?snake in cm?

2)2) 244 cm244 cm

2.44 m x 2.44 m x 100 cm 100 cm = 244 cm= 244 cm

1 m1 m

What isWhat is wrongwrong with with the following setup? the following setup?

1.4 day x 1.4 day x 1 day 1 day x x 60 min 60 min x x 60 sec 60 sec

24 hr 1 hr 1 min24 hr 1 hr 1 min

1.4 1.4 day day x x 1 1 dayday x x 60 min 60 min x x 60 sec 60 sec

2424 hr hr 1 1 hr hr 1 min 1 min

Units = Units = dayday22//hrhr22 Not the final unit neededNot the final unit needed

Steps to Problem SolvingSteps to Problem Solving

Read problemRead problem Identify data Identify data Write down a unit plan from the Write down a unit plan from the

initial unit to the desired unitinitial unit to the desired unit Select conversion factorsSelect conversion factors Change initial unit to desired Change initial unit to desired

unitunit Cancel units and checkCancel units and check Do math on calculator Do math on calculator Give an answer using Give an answer using

significant figuressignificant figures

If the ski pole is If the ski pole is 3.0 feet in length, 3.0 feet in length, how long is the how long is the ski pole in mm? ski pole in mm?

3.0 ft x 3.0 ft x 12 in 12 in x x 2.54 cm2.54 cm x x 10 mm10 mm = =

1 ft 1 in. 1 cm1 ft 1 in. 1 cm

Significant digits Significant digits The digits reported in a measured The digits reported in a measured

quantity quantity Indicate the precision of the Indicate the precision of the

measuring instrument measuring instrument Calculations should not have more Calculations should not have more

significant digits than the least significant digits than the least number of significant digits in the number of significant digits in the problem.problem.

Rules – Significant DigitsRules – Significant Digits 1. All nonzero numbers are 1. All nonzero numbers are

significant. Ex: 456 – 3 sig.significant. Ex: 456 – 3 sig. 2. All zeros between numbers are 2. All zeros between numbers are

significant. Ex: 408 – 3 sig.significant. Ex: 408 – 3 sig. 3. If decimal present, zero’s to the 3. If decimal present, zero’s to the

left are not significant. left are not significant. Ex: 0.0078 – 2 sig.Ex: 0.0078 – 2 sig.

4. If decimal present, zero’s to the 4. If decimal present, zero’s to the right are significant. right are significant. Ex: 0.090 – 2 sig.Ex: 0.090 – 2 sig.

5. If no decimal, zero’s on end are 5. If no decimal, zero’s on end are not significant. Ex: 34500 – 3 sig.not significant. Ex: 34500 – 3 sig.

Adding and SubtractingAdding and Subtracting

In addition and subtraction, round up In addition and subtraction, round up your answer to the least precise your answer to the least precise measurement or least number of measurement or least number of places behind the decimal.places behind the decimal.

For example: For example:

24.686 + 2.343 + 3.21 = 30.239 = 24.686 + 2.343 + 3.21 = 30.239 = 30.24 30.24

3.21 is the least precise 3.21 is the least precise measurement. measurement.

Multiplying and DividingMultiplying and Dividing

In multiplication and division, In multiplication and division, round it up to the least number round it up to the least number of significant digits. of significant digits.

For example: For example:

3.22 * 2.1 = 6.762 = 6.8 3.22 * 2.1 = 6.762 = 6.8 2.1 contains 2 significant digits. 2.1 contains 2 significant digits.

Scientific NotationScientific Notation

Used for expressing very large or Used for expressing very large or very small values very small values

standard formstandard form base x 10 base x 10 exponentexponent

base is between 1.0 and 9.999… base is between 1.0 and 9.999… if exponent is positive the value is greater than 1if exponent is positive the value is greater than 1

if exponent is negative the value is less than 1if exponent is negative the value is less than 1 convert to decimal by moving the convert to decimal by moving the

decimal the number of places decimal the number of places indicated by the exponent indicated by the exponent