Presentation on theme: "MATH for SCIENCE Conversion Problems Introduction"— Presentation transcript:
1 MATH for SCIENCE Conversion Problems Introduction A. In science many problems require conversions from one set of units to another. Some people use many proportions to do these conversions. This method can be quite confusing when there are multiple conversions to be done. The most efficient and easiest method to understand is called dimensional analysis or factor-label method.B.Dimensional analysis requires students to understand two concepts.1. All numbers must be used with their units. For example, mass of anobject would be 8 g and not just 8.
2 All standard or situational equivalents can be represented by two All standard or situational equivalents can be represented by two fractions. The choice depends on what units are originally given in the problem. For example:1 minute = 60 seconds 1 minute or seconds60 seconds minute1 foot = 12 inches foot or inches12 inches foot1 meter = 100 centimeter 1 meter or cm100 cm meter
3 3. This method can be used for problems that are one step, two steps, three steps, and more. It can accommodate any number of conversions as one linear problem, moving one step at a time. Each step directs the set-up for the next step until the goal units are reached.Problem Solving SchemeGiven Data x Specific Fractional Equivalents) = What You’re Looking ForThe units in the numerator of the first item (given data) determine the units for the denominator of the next fraction. When these units are the same, they will cancel each other out. This also chooses which one of the two forms of the specific fractional equivalents you will need to use.
4 C. One Step Conversions 1. How many minutes are in five hours? Given Data: 5 hrsFractional Equivalent:1 hour = 60 minutes 1 hour or min60 min hourLooking For: # minutesGiven Data x Specific Fractional Equivalent = Looking For5 hours x 60 min = 300 min1 hourNotice how the “hour” units canceled each other out.
5 If a turtle walked 20 yards in one hour, how many inches did he walk in that hour?Given Data: 20 yards/ 1 hourSpecific Fractional Equivalents:1 yard = 36 inches 1 yard or 36 in36 in yardLooking For: # inches/hourGiven Data x Specific Fractional Equivalent = Looking For20 yards x 36 inches = 720 inches1 hr 1 yard hr
6 A nugget of gold found in the river weighs 6.5 ounces. How many grams will that weigh?Given Data: 6.5 ozSpecific Fractional Equivalents:1 ounce = grams ounce or g28.33 g ounceLooking For: # gramsGiven Data x Specific Fractional Equivalent = Looking For6.5 ounces x grams = grams1 ounce
7 D. Two Step Conversions ~ Type 1 Remember, the units in the previous numerator will determinewhich form of the two Fractional Equivalents will be used.Two students were using a computer program for their research data. One of their study observations took 5 hours. Their computer program, however, will only let them enter the time in seconds. How many seconds should they enter?Given Data: 5 hoursSpecific Fractional Equivalents:1 hour = 60 minutes 1 hour or 60 min60 min 1 hour1 minute = 60 seconds 1 min or sec60 sec 1 minLooking For: # secondsGiven Data x Specific Fractional Equivalents = Looking For5 hours x 60 min x 60 sec = 18,000 sec1 hour min
8 2. Convert 2,250 grams to # pounds. Given Data: 2,250 gramsSpecific Fractional Equivalents:1 gram = ounces 1 gram or ozoz 1 gram16 ounces = 1 pound 16 oz or 1 lb 1 lb 16 ozLooking For: # pounds2,250 grams x oz x 1 lb = lbs1 gram oz
9 3. Convert 2.5 meters to # inches. Given Data: mSpecific Fractional Equivalents:1 meter = 3.28 feet 1 m or 3.28 ft3.28 ft 1 m1 foot = 12 inches 1 ft or 12 in12 in 1 ftLooking For: # inches2.5 m x ft x 12 in = in1 m ft
10 E. Two Step Conversions ~ Type 2 These problems involve converting not just the numerator given, but also the denominator.Do the usual conversion of the numerator.Then, convert the denominator. To do this, the units in theoriginal denominator determine the units in the later numerator Thus, by having the same units in the denominator and then inthe later numerator, the units once again will cancel each otherout.
11 1. Convert 50 miles/hour to # kilometers/minute. Given Data: 50 miles/hourSpecific Fractional Equivalents:1 mile = 1.61 km 1 mile or 1.61 km1.61 km 1 mile1 hour = 60 min 1 hr or 60 min60 min 1 hrLooking For: # km/min2.5 miles x km x 1 hr = km1 hr mile min min
12 Convert 20 yards/min to # inches/sec. Given Data: 20 yd/minSpecific Fractional Equivalents:1 yard = 36 inches 1 yd or 36 in36 in 1 yd1 minute = 60 seconds 1 min or 60 sec60 sec 1 minLooking For: # inches/second20 yd x 36 in x 1 min = 12 in1 min 1 yd sec sec
13 3. Convert 100 ounces/gallon to # grams/liter. Given Data: 100 oz/galSpecific Fractional Equivalents:1 gram = ounces or 1 ounce = grams1 liter = gallons or 1 gallon = litersLooking For: # grams/liter100 oz x 1 gram x gal = grams1 gal oz L LOR100 oz x g x 1 gal = grams1 gal oz L L
14 Three Step Conversion Problems Remember, the units in the previous numerator will determine which form of the two fractional equivalents will be used.Some problems may also include changing the denominator’s units as well. The same sequence of actions apply: First, change the numerator’s units then change the denominator’s units.
15 60 sec 1 min 1. Convert 3 days to # seconds. Given Data: 3 daysSpecific Fractional Equivalents:1 day = 24 hours 1 day or 24 hrs24 hrs 1 day1 hour = 60 minutes 1 hr or 60 min60 min 1 hr1 minute = 60 seconds 1 min or 60 sec60 sec 1 minLooking For: # seconds3 days x 24 hrs x 60 min x 60 sec = 25,920 seconds1 day hr min
16 2. Convert 18 kilometers/hour to # meters/second. Given Data: 18 km/hrSpecific Fractional Equivalents:1 km = 1,000 m 1 km or 1,000 m1,000 m 1 km1 hr = 60 min1 min = 60 secLooking For: meters/second18 km x 1,000 m x 1 hr x 1 min = 5 m1 hr km min sec sec
17 3. Convert 9,000 grams/centimeter to # pounds/inch. Given Data: 9,000 g/cmSpecific Fractional Equivalents:28.33 g = 1 oz g or oz1 oz g16 oz = 1 lb 16 oz or lb1 lb oz2.54 cm = 1 in cm or in1 in cmLooking For: lb/in9,000 g x 1 oz x 1 lb x cm = lb1 cm g oz in in