1. DIMENSIONAL ANALYSIS DIMENSIONAL ANALYSIS A.K.A FACTOR-LABELING USING UNITS TO SOLVE A MATH PROBLEM

2. 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

3. HOW TO USE IDENTIFY THE GIVEN AND THE UNKNOWN. WRITE DOWN THE APPROPRIATE CONVERSION FACTOR(S) TO USE. (OR PLUG NUMBERS INTO THE FORMULA)

4. 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

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

6. 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

7. 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.

8. CANCEL UNITS. IF THE UNITS CANCEL THEN YOU CAN DO THE MATH. SIG. FIGS. COME FROM THE GIVEN.

9. 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

10. 76.0 m x 1 ft x 1 yd = 1 0.3048 m 3 ft CALC. ANS: 83.11461067 yds ROUNDED ANS: 83.1 yds UNKNOWN UNIT

11. PRACTICE PROBLEMS COPY AND WORK 1) The density of an object is 7.71 g/mL. Its mass is 51.12g. What volume does the object occupy?

12. 2) A box has a mass of 4.5 kg and a volume of 6.4L. Calculate the density in g/cm 3. Use dimensional analysis to convert your metric units.

13. ANSWERS 1) D = 7.71g/mL m = 51.12g v = ? D = m v solve for this

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

15. PROBLEM 2 REQUIRES 3 STEPS: –1 ST CONVERT kg TO g –2 ND CONVERT L TO cm 3 –USE DENSITY EQUATION

16. 2) GIVEN: 4.5kg UNK: g UNK: g C.F.: 1kg = 1000g C.F.: 1kg = 1000g 4.5kg X 1000g = 4500g 1 1kg

17. GIVEN: 6.4L GIVEN: 6.4L UNK: mL UNK: mL C.F.:1L = 1000 mL C.F.:1L = 1000 mL 1mL = 1cm 3 1mL = 1cm 3 6.4L X 1000mL X 1 cm 3 = 1 1L 1mL 6400cm 3

18. WORK: D = m/v D= 4500g = 6400cm 3 0.70g/cm 3