Measures of Time The clock is the standard instrument for measuring time. The earth turns round on its axis once in a day. For convenience in estimating shorter periods of time, a day is divided into hours, minutes and seconds. In measuring longer periods of time the days are grouped into weeks, months and years. Table of Time = 60 seconds (sec.)=1 minute (min.) 60 minutes = 1 hour (hr.) 7 days=1 week (wk.) 365 days=1 year 366 days=1 leap year The earth travels around the sun in approximately 3651 days. In order to save the inconvenience of having a fractional part of a day left each year, we provide an extra day every 4 years. We call a year containing this extra day a "leap year." 10 years are known as a decade. 100 years are called a century. The following rhyme will help you in remembering the number of days in each month: “Thirty days hath September 'Till leap year gives it twenty-nine.” The old expression in fine meant in small amount. Exercise 7 1. How many minutes are there in 4 hours? 3. In a certain city school system the school day in the high school is divided into 7 forty-five minute periods. How many hours is the high school in session, not counting the noon intermission? 4. In Belgium the clocks mark every hour from 1 to 24 Which is better, the Belgian plan or ours? 5. When a clock face is divided into twelve hour spaces, each one is how much larger than one of the spaces on a twentyfour hour clock face of the same size? 6. Find the number of seconds in a day. 7. What is meant by the expression 9:00 A. M.; by 3:30 P. M.? 8. Fifteen minutes each day devoted to some plan of selfimprovement will amount to how much time in a year? 9. A train running 40 miles an hour goes how many feet per minute? How many feet per second? 10. The Mauretania made the voyage from Queenstown to New York, a distance of 2800 miles, in 4 days, 10 hours and 48 minutes. Find the total number of minutes required for this voyage across the Atlantic Ocean. 11. The United States census is taken once every decade. How many times is a census taken in a century? 12. Any year divisible by 4 is a leap year except the century years, which must be divisible by 400 to be a leap year. Which of the following will be a leap year: 1924, 1925, 1926, 1960, 2000? a Exercise 8. Reduction of Denominate Numbers Numbers expressing measures are called denominate numbers. For example: 3 quarts, 4 feet, 8 cubic feet, 3 bushels, 7 acres and 15 pounds are denominate numbers. 1. A cow gives 3 gallons of milk at each milking. How many pint bottles can be filled from one milking? In finding the number of pints in 3 gallons, we have changed or reduced from higher units to lower units. In this process we have multiplied the number of higher units (3) by the number of the lower units (8) in one of the higher units. Reduce: 2. 4 bushels to pecks; to quarts; to pints. 3. 6 gallons to quarts; to pints; to half-pints. 4. 10 feet to inches; 5 feet to inches. 6. 2 rods to yards; to feet; to inches. 6. 2 tons to pounds; 8 pounds to ounces 7. 5 feet 7 inches to inches. Solution: 5 feet=5X12 inches=60 inches. 60 inches +7 inches 67 inches. 8. 10 feet 6 inches to inches. 9. 2 yards 3 feet to feet. 10. 1 ton 500 pounds to pounds. 11. 2 bushels 3 pecks to pecks. 12. 5 gallons 2 quarts to pints. 13. 5 yards 6 inches to inches. 14. 2 pounds 9 ounces to ounces. 16. 4 bushels 3 quarts to quarts. 16. 2 miles 80 rods to rods. 17. 3 pecks 5 quarts to quarts. 23. A bin measured 9 feet 4 inches long; 6 feet 8 inches wide and 5 feet 11 inches deep. Express these measurements in inches. Find the number of cubic inches in the bin. a Exercise 9 1. A school room measured 24 feet in width and 30 feet in length. Express the width and length of this room in yards. In finding the number of yards in 24 feet, we have changed or reduced from lower units to higher units of measure. In this process we divided the number of lower units (24) by the number of lower units (3) making a higher unit. Reduce: 2. 156 inches to feet. 3. 48 ounces to pounds. 4. 56 quarts to pecks. 5. 54 square feet to square yards. 6. 10,368 cubic inches to cubic feet. 7. 48 pints to gallons. 8. 22 yards to rods. 9. 64 quarts to bushels. 10. 320 square rods to acres. 11. 54 cubic feet to cubic yards. 12. 195 inches to feet and inches. Solution: 195 inches : 12 inches=16, with a remainder of 3 inches Then 195 inches=16 feet 3 inches. Change to higher units: 13. 54 inches 19. 67 cubic feet 14. 87 ounces 20. 137 square feet 16. 46 yards 21. 504 square inches 16. 61 pints 22. 27 pecks 17. 192 minutes 23. 89 feet 18. 1632 rods 24. 975 seconds 26. Washington monument is 555 feet high. Express its height in yards and feet. 26. A field measured 36 rods long and 24 rods wide. Find the area of this field in square rods. Express the area in acres and square rods. 27. A load of coal weighed 3725 pounds. Express the weight of this load in tons and pounds. Exercise 10 1. A dairyman bought 15 gallons of milk from a neighbor. How many quart bottles will that amount of milk fill? How many pint bottles will it fill? 2. This dairyman has customers who use 186 quarts and 122 pints of milk per day. How many gallons does he need each day to supply these customers? 3. A 10-pound box of salted peanuts is put into 4-ounce bags. How many such bags can be filled from the box? 4. During one month a family used 102 gallons of milk. How much was their milk bill at 14 cents per quart? |