Section 7 – 1 Converting U.S. Customary Units of Length Common ...

Basic College Mathematics (ALEKS)Chapter Seven MEASUREMENTSection 7 – 1Converting U.S. Customary Units of LengthCommon Units1 ft = 12 in 1 in = ft1yd = 3 ft1 ft = yd1 mi = 5280 ft1 ft = mi 1 mi = 1760 yd1 yd = mi Converting US Common Units of Length by Using Substitution6 ft in 6 x (1 ft) = 6 x ( ) = 6 x (12 in) = 72 in12.6 ft yd 12.6 x ( yd) = 4.2 ydConverting US Common Units of Length by Using Unit Ratios1 ft = 12 in = 1 = = 1 = Procedure:1. Numerator = new unit (to)2. Denominator = old unit (from)720 in ft 720 in x = 720 = 60 4224 ft mi 4224 = 0.8 8 mi yd 8 = 14080 1 Chapter 7

Basic College Mathematics (ALEKS)Chapter Seven MEASUREMENTMaking Multiple Conversions of LengthUsed when there is no direct conversion factors.1 year sec yr day min sec (road map)1 = 31,536,000 sec6.2 yd in yd ft in 6.2 yd x = 223.2 in6336 in mi in ft mi 6336 in = 0.1 mi Adding and Subtracting Mixed Units8’ 4” = 8 ft + 4 in4’ 10” = 4 ft + 10 inAdd LIKE units8’ 4” + 4’ 10” = (8 ft + 4 in)+( 4 ft + 10 in) = 12 ft + (14 in)12 ft + (1 ft + 2 in) = 13 ft + 2 in = 13’ 2”6’ 3” – 4’ 9” = (6 ft + 3 in) – (4 ft + 9 in) = (6ft – 4 ft) + (3 in – 9 in)2 ft + (3 in – 9 in) = 1 ft + (12 in + 3 in – 9 in) = 1 ft 6 in = 1’ 6”Applications:2 Chapter 7

Basic College Mathematics (ALEKS)Chapter Seven MEASUREMENTPerimeter = 3 ft + 6 yd + 3 ft + 6 yd (in feet)P = 6 ft + 12 yd = 6 ft + (12 yd ) = 6ft + 36 ft = 42 ft Cut 10 pieces of rope into 2 ft and3 in lengths. How much rope?Repeated addition = multiplication10 x (2 ft + 3 in) =10 x 2 ft + 10 x 3 in =20 ft + 30 in =20 ft + 12 in + 12in + 6in =22 ft + 6 in = 22’ 6”12’ 6” length of ribbon is cut into 3pieces. Find the length?(12’ 6”) ÷ 3 = + "= 4’ 2” Section 7 – 2Converting U.S. Common Units of Time, Weightand CapacityTime Capacity Weight1 yr = 265 day 3 tsp = 1 T 1 pound = 16 oz1 wk = 7 day 1 cup = 8 fl oz 1 ton = 2000 pounds1 day = 24 hr 1 pint = 2 cup1 hr = 60 min 1 quart = 2 pint1 min = 60 sec 1 quart = 4 cup1 gal = 4 quart3 Chapter 7

Basic College Mathematics (ALEKS)Chapter Seven MEASUREMENTConvert:16 hr day 16 hr x = = day24 hr sec 24 hr x = 86,400 sec2:22:45 2 hr + 22 min + 45 sec min(2 hr 142.75 min) + (22 min) + = 120 min + 22 min + 0.75 min120 ton lb 120 T = 240,000 lb5 lb 12 oz oz 5 lb Triples weigh 4 lb 3 oz, 3 lb 9 oz,And 4 lb 5 oz. What is the totalweight?+ 12 = 80 oz + 12 oz = 92 oz4 lb+3 oz+3 lb+9 oz+4lb+5 oz11 lb + 17oz = 12 lb + 1 oz1 gal cup 1 1 gal pint 1 = 16 cup = 8 cup8.5 gal quart 8.5 = 34 2.25 qt cup 2.25 = 9 40 fl oz qt 40 = 1.25 qt Recipe calls for 3 cup. Jar holds24 fl oz. Is there enough in jar?3.5 cup xNO. = 28 4 Chapter 7

Basic College Mathematics (ALEKS)Chapter Seven MEASUREMENTSection 7 – 3Metric Units of LengthOne Letter: m = meter, g = gram, L = liter (UNIT)Two or more letters = Prefix + UnitConversion Ratios (always converts to meters, may take two steps)1 kilometer (km) * 1000 m1 hectometer (hm) 100 m1 dekameter (dam) 10 m1 meter * 1 m1 decimeter (dm) 0.1 m1 centimeter (cm) * 0.01 m1 millimeter (mm) * 0.001 m“*” ones most usedPrefix LineKids Have Doughnuts Until Dad Calls MomKilo Hecto Deka UNIT Deci Centi milli1000 100 10 1meter1 gram1 Liter0.1 0.01 0.001Procedure:1. Locate starting unit.2. Count number of positions needed to reach new unit.3. Move the decimal point the SAME DIRECTION the SAMENUMBER of positions.4. Change to new unit.864 cm m 864 . = 8.64 Prefix Line cm to M = 2 to LEFT 864 8.64 m5 Chapter 7

Basic College Mathematics (ALEKS)Chapter Seven MEASUREMENT8.2 km m 8.2 = 8200 Prefix Line km to m = 3 to Right8.2 8200 m11,033 m km 3 to Left 11.033 m24 m cm 2 to Right 2400 cm4000 m + 3500 m + 2500 m = howmany Kilometers?4000 m + 3500 m + 2500 m =10000 m km (3 to L)10.0 kmSection 7 – 4Metric Units of Mass, Capacity, and MedicalApplicationsMass80 kg g 3 to R 80,000 g49 cg g 2 to L 0.49 gCapacity Special case: 1 mL = 1 cm 3 = 1 cubic centimeter = 1 cc10.2 L cL 2 to R 1020 cL150,000 mL kL 6 to L 0.15 kL0.5 cc mL 1 to 1 0.5 mL0.04L cc 3 to R 40 mL = 40 ccReview64 km m 3 to R 64,000 m1420 mL L 3 to L 1.42 L680 g kg 3 to L 0.68 kg6 Chapter 7

Basic College Mathematics (ALEKS)Chapter Seven MEASUREMENTMedical (Special case: microgram = = 1 mcg,,mcg g 6 to Left mcg mg 3 to Leftg mcg 6 to Right mg mcg 3 to RightChild receives 0.5 mg per kg ofbody mass. If the child weighs 27kg, how much drug should childreceive?0.5 27 = 13.5 1 0.04 mg mcg 3 to R 40 mcg95,000 mcg mg 3 to L 95 mgSection 7 – 5Converting Between U.S. Common and Metric UnitsLength Weight/Mass Capacity1 in ≈ 2.54 cm 1 lb ≈ 0.45 kg 1 qt ≈ 0.95 L1 ft ≈ 0.305 m 1 oz ≈ 28 g 1 fl oz ≈ 30 mL ≈ 30 cc1 yd ≈ 0.914 m1 mi ≈ 1.61 km184 km mi 184 Round to one decimal place . = 114.28 = 114 (round nearest mile)4 m ft 4 . ≈ 13.11 ≈ 13.1 3 in cm 3 . 6500 yd m 6500 . 8 kg lb 8 . ≈ 7.62 ≈ 7.6 ≈ 5941.0≈ 17.778 ≈ 17.8 7 Chapter 7

Basic College Mathematics (ALEKS)Chapter Seven MEASUREMENT4 T kg 4 . ≈ 3600 120 mL fl oz 120 ≈ 4 4 qt L 4 . ≈ 3.8 A 720 mL bottle sells for $0.79.32 oz bottle sells for $1.29.Compare the price per oz.720 mL x = 24 fl oz$. = $0.033$. = $0.040720 mL bottle best price800 meter race is shorter than a 0.5miles. How many yards less is it?Round to yard. 0.5 mi x 805 – 800 = 5 yd = 805 Units of TemperatureConvert 0 C to 0 FF = + 32F = 1.8C + 32Convert 0 F to 0 CC = − 32)C = .84 0 F 0 C C = 84 − 32) = 52 = 28.9 ℃ 10 ℃ ℉ F = 10 + 32 = 18 + 32 = 50 ℉8 Chapter 7