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Q1. From the figure on the right, find the age of Mr. Wong. - They both are my sisters. One is 1 year younger than me and the other is 2 years younger than me. - If the sum of our ages is represented by a binary number, each digit of the number is 1.Q2. There are 64 squares... 顯示更多 Q1. From the figure on the right, find the age of Mr. Wong. - They both are my sisters. One is 1 year younger than me and the other is 2 years younger than me. - If the sum of our ages is represented by a binary number, each digit of the number is 1. Q2. There are 64 squares on a chessboard. Suppose one grain of rice is put on the first square, and rice is subsequently put on the other 63 squares such that the number of grains on a square is twice that on the previous one. (Express the answers in (a) and (b)(i) in scientific notation, and give the answers correct to 3 significant figures.) a.) Calculate the number of grains of rice on the 64th square. b) (i) Given that the weight of grain of rice is 0.2g, what is the total weight in g of the rice on the 64th square? (ii) Suppose each Chinese on average eats 200 g of rice every day. The current population of China is 1.3 billion (assume it remains unchanged). For how many years can the rice on the 64th square feed all the people in China? (Take 1 year = 365 days and give the answer correct to the nearest 100 years.) Q3. (a) Convert the first three multiples of 4 into binary numbers. (b) By observing the results in (a), write down the characteristic of the binary numbers which are equivalent to the multiples of 4. (c) Using the result in (b), write down the largest 6-digit binary number which is a multiple of 4.
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MATHS (LAWS OF indices)
發問:
Q1. From the figure on the right, find the age of Mr. Wong. - They both are my sisters. One is 1 year younger than me and the other is 2 years younger than me. - If the sum of our ages is represented by a binary number, each digit of the number is 1.Q2. There are 64 squares... 顯示更多 Q1. From the figure on the right, find the age of Mr. Wong. - They both are my sisters. One is 1 year younger than me and the other is 2 years younger than me. - If the sum of our ages is represented by a binary number, each digit of the number is 1. Q2. There are 64 squares on a chessboard. Suppose one grain of rice is put on the first square, and rice is subsequently put on the other 63 squares such that the number of grains on a square is twice that on the previous one. (Express the answers in (a) and (b)(i) in scientific notation, and give the answers correct to 3 significant figures.) a.) Calculate the number of grains of rice on the 64th square. b) (i) Given that the weight of grain of rice is 0.2g, what is the total weight in g of the rice on the 64th square? (ii) Suppose each Chinese on average eats 200 g of rice every day. The current population of China is 1.3 billion (assume it remains unchanged). For how many years can the rice on the 64th square feed all the people in China? (Take 1 year = 365 days and give the answer correct to the nearest 100 years.) Q3. (a) Convert the first three multiples of 4 into binary numbers. (b) By observing the results in (a), write down the characteristic of the binary numbers which are equivalent to the multiples of 4. (c) Using the result in (b), write down the largest 6-digit binary number which is a multiple of 4.
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Q1. From the figure on the right, find the age of Mr. Wong.- They both are my sisters. One is 1 year younger than me and the other is 2 years younger than me.- If the sum of our ages is represented by a binary number, eachdigit of the number is 1.A. Let the age of Mr. Wong be x.The sum of their age = 3x-311(2) = 3(10)3x-3 = 33x = 6x = 21111(2) = 15(10)3x-3 = 153x = 18x = 6111111(2) = 63(10)3x-3 = 633x = 66x = 22......From the above, it is deduced that if the number of digits of a number can be divided by 2 and each digit of the number is 1, there is a solution for x.So, there are infinite answers. (I can only conclude this because I don’t have the figure.)Q2. There are 64 squares on a chessboard. Suppose one grain of rice is put on the first square, and rice is subsequently put on the other 63 squares such that the number of grains on a square is twice thaton the previous one.(Express the answers in (a) and (b)(i) in scientific notation, and givethe answers correct to 3 significant figures.)a.) Calculate the number of grains of rice on the 64th square.A. number of grains of rice on the 64th square= 2^(64-1)= 2^63= 9.22*10^18(cor. to 3 sig. fig.)b) (i) Given that the weight of grain of rice is 0.2g, what is the total weight in g of the rice on the 64th square?A. the total weight= 2^63 *0.2= 1.84*10^18(cor. to 3 sig. fig.)(ii) Suppose each Chinese on average eats 200 g of rice everyday. The current population of China is 1.3 billion (assumeit remains unchanged). For how many years can the rice onthe 64th square feed all the people in China?(Take 1 year = 365 days and give the answer correct to thenearest 100 years.)A. number of years= 0.2*2^63 / (200*1300000000*365*100)= 200(cor. to the nearest 100 years)Q3. (a) Convert the first three multiples of 4 into binary numbers.A. 4(10) = 100(2)8(10) = 1000(2)12(10) = 1100(2)(b) By observing the results in (a), write down the characteristic ofthe binary numbers which are equivalent to the multiples of 4.A. The last two digits are 0.(c) Using the result in (b), write down the largest 6-digit binary number which is a multiple of 4.A. 111100(2) = 60 2010-10-17 01:55:03 補充： Q1. A. Let the age of Mr. Wong be x. The sum of their age = 3x-3 11(2) = 3(10) 3x-3 = 3 3x = 6 x = 2 1111(2) = 15(10) 3x-3 = 15 3x = 18 x = 6 111111(2) = 63(10) 3x-3 = 63 3x = 66 x = 22 ...... 2010-10-17 01:55:59 補充： From the above, it is deduced that if the number of digits of a number can be divided by 2 and each digit of the number is 1, there is a solution for x. So, there are infinite answers. (I can only conclude this because I don’t have the figure.) 2010-10-17 01:56:21 補充： Q2. a.) Calculate the number of grains of rice on the 64th square. A. number of grains of rice on the 64th square = 2^(64-1) = 2^63 = 9.22*10^18(cor. to 3 sig. fig.) 2010-10-17 01:56:38 補充： (b) (i) Given that the weight of grain of rice is 0.2g, what is the total weight in g of the rice on the 64th square? A. the total weight = 2^63 *0.2 = 1.84*10^18(cor. to 3 sig. fig.) (ii) A. number of years = 0.2*2^63 / (200*1300000000*365*100) = 200(cor. to the nearest 100 years) 2010-10-17 01:56:48 補充： Q3. (a) Convert the first three multiples of 4 into binary numbers. A. 4(10) = 100(2) 8(10) = 1000(2) 12(10) = 1100(2) (b) By observing the results in (a), write down the characteristic of the binary numbers which are equivalent to the multiples of 4. A. The last two digits are 0. 2010-10-17 01:56:55 補充： (c) Using the result in (b), write down the largest 6-digit binary number which is a multiple of 4. A. 111100(2) = 60其他解答:
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