Decimal Fractions and Common Fractions To change a decimal fraction to a common fraction: 1. Change .125 to a common fraction in its lowest terms. .125 = 1000 Since in a decimal fraction the denominator is understood, we need simply change the decimal fraction to the form of a common fraction, and then reduce it to lower terms if possible. To change a common fraction to a decimal fraction: 17. Change to a decimal fraction. Annex decimal ciphers to the numerator and divide by the denominator. If there still is a remainder, continue to annex ciphers as far as desired. In some cases the change may be made at sight by changing the fraction so that its denominator will be some multiple of 10. French and German Money In French money 100 centimes make a franc. A franc equals $0.193 in United States money. In German money 100 pfennigs equal a mark. A mark equals $0.2385 in United States money. 1. About how many centimes are equivalent to a cent in United States money? 2. What is the exact equivalent of a centime in United States money? 3. Find the value in United States money of 20 francs, 60 centimes. 4. Find the exact value in French money of 25%. Of $1. Of $5. 5. About how many German pfennigs are equivalent to a cent? 6. What is the exact equivalent of a pfennig in United States money? 7. Find the value in United States money of 10 marks, 50 pfennigs. 8. Find the value in German money of 40 . Of $30. Find the exact value of the following in United States money: 9. 35 centimes 10. 75 centimes 11. 200 francs 12. 64 pfennigs 13. 800 marks 14. 25 francs, 30 centimes 15. 150 francs, 12 centimes 16. 1250 francs, 40 centimes 17. 15 marks, 30 pfennigs 18. 2520 marks, 60 pfennigs Find the value of the following in French money: Find the value of the following in German money : Percentage Discounts of 25% and 20% on $200 100%$200 75%=$150 100% $150 80%=$120 Goods are sometimes subject to two or three discounts below the list price when sold. Such discount is called commercial discount or trade discount. 1. If shoes listed at $4.00 a pair are discounted 20%, what is the discount price? 80% of $4 = ? 2. If the shoes are again discounted at 10% below the first discount price, what is the second discount price? 80% of 84 x 90% = ? 3. What would have been the price if the shoes had been discounted but once at 30%? 4. What is the selling price of goods listed at $1.00 and subject to discounts of 25% and 20% ? 75% of $1.00 × 80% = ? 5. A wholesale merchant sold a bill of goods. The list price was $480 and the discounts 163% and 10%. What was the net amount of the bill? 6. Find the difference between the net amounts of a bill of goods for $400 if sold at trade discounts of 25% and 15%, or at a single discount of 40%. 7. If I should buy goods which are listed at $500, at 20% below the list price, and sell them at 10% below the list price, how much should I gain? 8. What per cent should I gain on what they cost me? Miscellaneous Problems 1. If 12 gas burners, each of which consumes 5 cu. ft. of gas an hour, are burned 3 hours each night, what will be the cost of the gas for a year of 365 days, at $1.25 a thousand feet? 2. What is the circumference of a wheel that revolves 3820 times in going 10 miles? 3. How many feet of lumber are there in 12 scantlings, each 4 inches square at the end, and 15 feet long? 4. What principal will gain $51.20 in 3 yr. 2 mo. 12 da. at 5%? 5. What principal will amount to $500 in 2 years at 6%? 6. What is the present worth of a note of $200 which is payable in one year without interest, if the use of money is worth 6%? The present worth is the principal which will amount to $200 in a year at 6%? Therefore it is $200 ÷ 1.06. 7. What is the present worth of a note which promises to pay $360 in six months, if money is worth 4%? 8. There are 231 cubic inches in a gallon. Find the weight of a gallon of water. 9. The specific gravity of a certain ore is 6.4. What would be the weight of a piece of the ore large enough to displace a gallon of water? 10. What would be the weight of the same piece of ore in water? 11. If the specific gravity of sea water is 1.026, what would be the weight in sea water of a cubic foot of metal whose specific gravity is 5.138 ? Square Root-Cube Root The square root of a number is equal to the product of one half of the factors in each of its groups of equal factors. The cube root of a number is equal to the product of one third of its factors. The fourth root is equal to the product of one fourth of the factors, etc. 1000 = 2 × 2 × 2 × 5 × 5 × 5. The square root of 324 is 2 × 3 × 3, The cube root of 1000 is 2 × 5, or 10. In this way it is easy to find a root of a number which is a perfect power, that is, a number whose root may be found without a remainder. 1. What are the smallest factors of 36? 2. What is the square root of 36? 3. What are the smallest factors of 216? 4. What is the cube root of 216? 5. Find the factors and the square root of 225. 8. Find the cube root of 5832. Of 27,000. 9. What is the fourth root of 810,000? 10. What is the length of one side of a square which contains 1764 sq. in. ? 11. What is the length of a square lot of land which contains 2025 sq. ft.? 12. Find the length of the edge of a cube which contains 13,824 cu. in. 13. Find the length of the hypotenuse of a right triangle, whose sides are 72 ft. and 54 ft. 14. Find the length of the edge of a cube, whose volume is equal to the volume of a rectangular solid which is 8' x 4' x 2'. |