Mullis1 GETTING FROM ONE UNIT TO ANOTHER: Dimensional Analysis aka. Factor Labeling Method

Mullis2 The answer is of ???????

Mullis3 You must indicate the units for a number to be meaningful. 150 pounds is not equal to 150 kg. With no unit, a numerical answer is incorrect!

Mullis4 Conversion factors A conversion factor is used to move from one unit to the other. We use a conversion factor by showing equivalent amounts in each unit, one over the other. –The top must be equal to the bottom. –Write the unit on bottom that you need to cancel out, or get rid of. Example: 12 eggs = 1 dozen eggs 12 eggs 1 dozen eggs How many eggs in 4 dozen? 4 dozen 12 eggs =48 eggs 1 dozen

Mullis5 Steps in Dimensional Analysis Identify needed conversion factor. Write what you have. Draw a grid to separate each factor. Write first conversion factor so that the unit you want to cancel out is on bottom. Cross out units (NOT the numbers) as they cancel out. When the top unit is what you want, multiply the numbers on top of grid, then divide by each number on the bottom of grid.

Mullis6 Dimensional Analysis Example: What is the weight of a 201 pound person in kg? Identify needed conversion factor. 2.2 lb = 1 kg Write what you have. 201 lb Draw a grid to separate each factor. Write first conversion factor so that the unit you want to cancel out is on bottom. 201 lb 1 kg 2.2 lb Cross out units (NOT the numbers) as they cancel out. When the top unit is what you want, multiply the numbers on top of grid, then divide by each number on the bottom of grid. 201 lb 1 kg =201 kg = 91.4 kg 2.2 lb2.2

Mullis7 Dimensional Analysis Example: How many km/sec is the same as 55 miles per hour? 1 km = 0.62 mile 60 min = 1 hour 60 sec = 1 min 55 mile 1 km 1 hr 1 min = hr 0.62 mile 60 min 60 sec 55 km x 1 x 1 x 1 = km 0.62 x 60 x 60 sec sec

Significant Figures All digits 1-9 inclusive are significant. Zeros between significant digits are always significant. –Example: has 4 significant figures. If a number contains a decimal point, all zeros and digits are significant after & including the first digit 1-9. –Trailing zeros in a number are significant in a number only if the number contains a decimal point has 4 sig. figs. Ex: 100 has 1 sig. fig. –Zeros in the beginning of a number whose only function is to place the decimal point are not significant. Ex: has 2 sig. figs. –Zeros following a decimal significant figure are significant. Ex: has 3 sig. figs. Ex: has 5 sig. figs. 8

Scientific Notation 1 Example 1: Convert to scientific notation. Move the decimal point so that there is only one digit to its left (a total of 6 places) = 1.5 x 10 6 Example 2: Convert to scientific notation. Move the decimal point 4 places to the right = 2.5 x Mullis9

Scientific Notation 2 Example 3: Correct 12 x 10 8 to proper scientific notation. Move the decimal one place to the left. Add to exponent when decimal moves left; subtract from the exponent when decimal moves right (ALSR). 12 x 10 8 = 1.2 x 10 9 Example 4: Correct x to proper scientific notation. Subtract from the exponent when decimal moves right, so = x = 4.00 x