DIMENSIONAL DIMENSIONAL ANALYSISANALYSIS

DIMENSIONAL DIMENSIONAL ANALYSISANALYSIS

A.K.A FACTOR-LABELINGA.K.A FACTOR-LABELING

USING UNITS TO SOLVE A USING UNITS TO SOLVE A MATH PROBLEMMATH PROBLEM

TYPES• USE A FORMULA OR • CONVERSION FACTORS

–SHOW A RELATIONSHIP BETWEEN DIFFERENT UNITS OF MEASUREMENT

–EX: 12 in = 1 ft 1 in = 2.54 cm

100 cm = 1 m 1 kg = 2.2 lbs

HOW TO USE• IDENTIFY THE GIVEN AND

THE UNKNOWN.•WRITE DOWN THE

APPROPRIATE CONVERSION FACTOR(S) TO USE. (OR PLUG NUMBERS INTO THE

FORMULA)

TO SOLVE (WHEN USING A FORMULA)

• IDENTIFY THE GIVENS AND UNKNOWN.• SUBSTITUTE THE GIVENS INTO THE

FORMULA• REARRANGE THE FORMULA TO SOLVE

FOR THE UNKNOWN

EXAMPLE •THE MASS OF AN OBJECT IS 5.87g AND THE VOLUME IS 7.98mL. WHAT IS THE DENSITY OF THE OBJECT?

IDENTIFY GIVEN & UNKNOWN D = ? m = 5.87 g D = m/v v = 7.98 mL SUBSTITUTE THE NUMBERS

D = 5.87g = 0.736 g/mL 7.98mL

TO SOLVE (WHEN USING CONVERSION FACTORS)

• PUT YOUR GIVEN OVER 1. (THIS TURNS IT INTO A FRACTION)

• MULTIPLY THE GIVEN BY THE APPROPRIATE CONVERSION FACTOR(S). THE UNITS TELLYOU WHICH CONVERSION FACTOR TO USE & HOW TO SET IT UP.

• CANCEL UNITS. IF THE UNITS CANCEL THEN YOU CAN DO THE MATH.

• SIG. FIGS. COME FROM THE GIVEN.

EXAMPLE •A WOMAN NEEDS 76.0 m OF

FABRIC. HOW MANY YARDS IS THIS?–GIVEN: 76.0 m–UNKNOWN: ? YARDS–CONVERSION FACTOR(S)CONVERSION FACTOR(S): 0.3048 m = 1 ft 3 ft = 1 yd

•76.0 m x 1 ft x 1 yd = 1 0.3048 m 3 ft

CALC. ANS: 83.11461067 ydsROUNDED ANS: 83.1 yds

UNKNOWN UNIT

PRACTICE PROBLEMSCOPY AND WORK

1) The density of an 1) The density of an object is 7.71 g/mL. Its object is 7.71 g/mL. Its mass is 51.12g. What mass is 51.12g. What volume does the object volume does the object occupy?occupy?

2) A box has a mass of 2) A box has a mass of 4.5 kg and a volume of 4.5 kg and a volume of 6.4L. Calculate the 6.4L. Calculate the density in g/cmdensity in g/cm33. Use . Use dimensional analysis to dimensional analysis to convert your metric convert your metric units.units.

•ANSWERS

•1) D = 7.71g/mL m = 51.12g v = ?

D = m v solve for this

WORK: v = m D v = 51.12g 6.63 mL 7.71g/mL

=

•PROBLEM 2 REQUIRES 3 STEPS:–1ST CONVERT kg TO g–2ND CONVERT L TO cm3

–USE DENSITY EQUATION

2)2) GIVEN: 4.5kg GIVEN: 4.5kg

UNK: gUNK: g

C.F.: 1kg = 1000g C.F.: 1kg = 1000g

4.5kg X 1000g = 4500g 1 1kg

GIVEN: 6.4LGIVEN: 6.4L

UNK: mLUNK: mL

C.F.:1L = 1000 mL C.F.:1L = 1000 mL

1mL = 1cm1mL = 1cm33

6.4L X 1000mL X 1 cm3 = 1 1L 1mL

6400cm3

WORK: D = m/v D= 4500g = 6400cm3 0.70g/cm3