Measuring and Calculating Chapter 1

Measurement Comparing an unknown quantity to a known standard Things we measure are called dimensions Length, mass, volume, temperature Each dimension has multiple units Meter, gram, liter, degree Celsius All measurements consist of a number and a unit.

Metric System Based on increments of 10 Only type of measurement used in science classes

Base Units Units assigned to each of the 7 dimensions Length – meter Mass – kilogram Time – second Temperature – kelvin Number of particles – mole Electrical current – ampere Light intensity - candela

Derived Units Units made by combining base units Area – m2 Density – kg/m3

Metric Prefixes King Henry Died by Drinking Chocolate Milk 7 cm = _____ Hm 30 kg = ____________ mg 45.76 m = ________cm

Unit Conversions/ Dimensional Analysis A way to convert from one unit to another. Converted units must measure the same dimension.

Bridge Method/ Train Track Example How many inches are in 3 miles? Draw a train track Identify beginning information Write measurement as a fraction 3 miles 1

Bridge Method/ Train Track Example How many inches are in 3 miles? We are going from a larger measurement to a smaller one. Find a conversion factor you know that changes miles into something smaller. 5280 feet = 1 mile 3 miles 1

Bridge Method/ Train Track Example How many inches are in 3 miles? 5280 feet = 1 mile Write your conversion factor on the track so that miles cancels out and you are left with the unit feet. 3 miles 1 5280 feet 1 mile

Bridge Method/ Train Track Example How many inches are in 3 miles? Is the unit you are looking for feet? What is the conversion factor to convert from feet to inches? 1 foot = 12 inches 3 miles 1 5280 feet 1 mile 12 inches 1 foot

Bridge Method/ Train Track Example How many inches are in 3 miles? Multiply all numbers on the top Divide all numbers on the bottom 3 x 5280 x 12 ÷1 ÷ 1÷ 1 = 190080 inches 3 miles 1 5280 feet 1 mile 12 inches 1 foot

Scientific Notation A base number that is multiplied by a factor of 10 Base x 10exponent To write the number out in long notation, move the decimal to left or right according to the exponent. 3 x 108 = 300,000,000 3 x 10-8 = .00000003 The base number must be between 1 and 10

Scientific Notation Write these in long notation 2 x 103 3 x 10-4

Scientific Notion Adding/Subtracting Multiplying Dividing Write out in long notation, do the math, put back in scientific notation Multiplying Multiply the bases, add the exponents Dividing Divide the bases, subtract the exponents

Scientific Notation 3 x 104 and 4 x 102

Limitations of Measurement Accuracy How close your measurements are to the actual or accepted value Precision How close your measurements are to each other

Percent Error A way to determine how accurate your measurements are |Your value – real value| ÷ real value x 100%

Scientific Problem Solving Read the problem Determine method of solution Choose the specific tools Set up the problem, estimate and calculate Check and format