Maths-
General
Easy
Question
Without doing any actual division, find which of the following is a terminating decimal or not:![6 over 125](data:image/png;base64,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)
Hint:
Hint:
Numbers with a fixed or finite number of digits following the decimal point are known as terminating decimals and numbers with infinite decimal places are known as non-terminating decimals.
The correct answer is: Terminating decimal expansion.
Let x = p/q be a rational number such that the prime factorisation of q is in form 2m5n, where m and n are non-negative integers, then x will have a terminating decimal expansion.
![x equals 6 over 125](data:image/png;base64,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)
In the given rational number, the value of q is 125. The factorisation of 125 is given as
Final Answer:
As the factorisation of 125 is in the form of 2m5n,
will have terminating decimal expansion.
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Find the values of a and b
If
Find the values of a and b
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Maths-General
Maths-
Nina, Shanti and Belle run a 1000 m race at a constant speed. When Nina crossed the finish line first, she was 200 m ahead of Shanti and 400 m ahead of Belle. When Shanti crossed the finish line, how far ahead of Belle was she?
Nina, Shanti and Belle run a 1000 m race at a constant speed. When Nina crossed the finish line first, she was 200 m ahead of Shanti and 400 m ahead of Belle. When Shanti crossed the finish line, how far ahead of Belle was she?
Maths-General
Maths-
The wheels on Charlie’s bike have a circumference of 1.5 m. When Charlie is riding fastest, the wheels rotate at a speed of five turns per second. a) What is the fastest speed Charlie can ride his bike, in km/h? b) How far would Charlie travel in 5 minutes at his fastest speed?
The wheels on Charlie’s bike have a circumference of 1.5 m. When Charlie is riding fastest, the wheels rotate at a speed of five turns per second. a) What is the fastest speed Charlie can ride his bike, in km/h? b) How far would Charlie travel in 5 minutes at his fastest speed?
Maths-General
Maths-
Walter and William have a height ratio of 7:8. If William has a height of 152 cm, how tall is Walter?
Walter and William have a height ratio of 7:8. If William has a height of 152 cm, how tall is Walter?
Maths-General
Maths-
A saltwater swimming pool requires 2 kg of salt to be added for every 10000 litres of water. Joan’s swimming pool is 1.5 metres deep, 5 metres wide and 15 metres long. How much salt will she need to add to her pool?
A saltwater swimming pool requires 2 kg of salt to be added for every 10000 litres of water. Joan’s swimming pool is 1.5 metres deep, 5 metres wide and 15 metres long. How much salt will she need to add to her pool?
Maths-General
Maths-
The Bionic Woman gives Batman a 12 second start in a 2 kilometre race. If the Bionic Woman runs at 5 km/min, and Batman runs at 3 km/min, who will win the race and by how many seconds
The Bionic Woman gives Batman a 12 second start in a 2 kilometre race. If the Bionic Woman runs at 5 km/min, and Batman runs at 3 km/min, who will win the race and by how many seconds
Maths-General
Maths-
At a school camp there is enough food for 150 students for 5 days. a) How long would the food last if there were only 100 students? b) If the food ran out after only 4 days, how many students attended the camp?
At a school camp there is enough food for 150 students for 5 days. a) How long would the food last if there were only 100 students? b) If the food ran out after only 4 days, how many students attended the camp?
Maths-General
Maths-
Michelle can complete a landscaping job in 6 days and Danielle can complete the same job in 4 days. Working together, in how many days could they complete the job?
Michelle can complete a landscaping job in 6 days and Danielle can complete the same job in 4 days. Working together, in how many days could they complete the job?
Maths-General
Maths-
The required staff to student ratio for an excursion is 2 : 15. If 10 teachers attend the excursion, what is the maximum number of students who can attend?
The required staff to student ratio for an excursion is 2 : 15. If 10 teachers attend the excursion, what is the maximum number of students who can attend?
Maths-General
Maths-
Julie and Jeanette enjoy finishing their 6 km morning run together. Julie runs at an average speed of 10 km/h and Jeanette runs at an average speed of 3 m/s. If Julie leaves at 8 a.m., at what time should Jeanette leave if they are to finish their run at the same time?
Julie and Jeanette enjoy finishing their 6 km morning run together. Julie runs at an average speed of 10 km/h and Jeanette runs at an average speed of 3 m/s. If Julie leaves at 8 a.m., at what time should Jeanette leave if they are to finish their run at the same time?
Maths-General
Maths-
Find the values of a and b : ![fraction numerator 5 plus 3 square root of 2 over denominator 5 minus 3 square root of 2 end fraction equals a plus b square root of 2](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJgAAAAuCAYAAADUUdBJAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAAA6JJREFUeNrtnDFoFEEUhpcgQSSIoiJBIUEsgogIGlRUJCAhiEgIFzBYSMBCrMRGIQYVCzsVrURBLFQIMaYQtZEgIqKFBiuJiJWEcKAQJB5Bjf8jT1yXvcvMbWbvduf/4Cd3w9zOZffdzHvzhhcE+aIJmksgQipyGBrjbSCueAId420gLlgNfdO/pM5J00/pgB5DM1AJmoCuQqssr3McehjTvhsahqahWWgcOsJHXHsDSwvxmXqgxlDbVuhpFdcpxLQ/h/o0ABA2QS+1jWTYwJJeY9qibytUhJYa9m+B3vMx+2tgG6APFv3PQDctxyjxMftnYGuhfvXDDlh87h3UZdF/ly6TpIYGNqvLlDjgp0I+jAsDiwYSJ8v0i/sOm6FJaInhWLKMvlbnn9QYeWjboEFdstqqjDxNI9CVULcawL5Q+0botl5jT+Qzl6Arhv+PXH8U6uSjrT86NSJLY5ltUiP7y1k1MNnnehPp+xnabujXjaqxErtnkVr6rZSSgZUb6wT0W301YSf00WB5bNMgYBntxZrU0m/i63xKycC2qKMfh2zI3tPX16HzBoHDkIWPRv7HSfptRCOtBlWXGlePAwOTZbdXDUDG6tBl72iZ/regH9q/uIBfKDwy6EPicZZ+69UZ5Cf0VWeAdkf/xF41gpJKpuODFfqvgH5BD6BXVUSovhzPmdEfbBK8Tb+9WGA7w3ckkFmMTIW36bd2NbD1HhmNzYwrWz33E47XGniefitk7PvKcnUBmgotKy2ODOwcNKDjTYZcj2aLazD9VqNZpNp9H/EzrwXzm70N6td2OzKwIQ3KTofGu2w5qzH9liH69KGHuRPY5VttDGxC/aIwy4P4Eyqppd/mKGfR5Zj+wqOOcouD2bJBI8g4I5iOBAJMv+VkiYxuGcjr746c/B1B/M67GPiz0Hum33JEMWYf6a0jA+tTw4kiJ2IGY9qZfssBXyLhvjzoYUcGJoFEf6StUbcQmivMsEy/ZZiL0A1dGsXvuhvMn7NzYWAj6uTv1/frtK2/wmeYfssBA/qrH9TZbMpym8IUue6h4F+qb9xgHKbfDMlS6YA1dXbvmH4zgKUDqsfH9Js1LB2QjAJvQXlYOiBDsHQAcW5gacHSATSwmsDSATQwZ7B0AA3MCSwd4JGBJS0dkCSoYOkAT2DpAJIatqUDksDSAZ5SqvFYPLuUY2xLBySBpQNyzmKUDjCFpQM8hKUDiNfw7BJxCs8uEefw7FIG+AN/C+G33s4/CQAAAR50RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1yb3c+PG1uPjU8L21uPjxtbz4rPC9tbz48bW4+MzwvbW4+PG1zcXJ0Pjxtbj4yPC9tbj48L21zcXJ0PjwvbXJvdz48bXJvdz48bW4+NTwvbW4+PG1vPiYjeDIyMTI7PC9tbz48bW4+MzwvbW4+PG1zcXJ0Pjxtbj4yPC9tbj48L21zcXJ0PjwvbXJvdz48L21mcmFjPjxtbz49PC9tbz48bWk+YTwvbWk+PG1vPis8L21vPjxtaT5iPC9taT48bXNxcnQ+PG1uPjI8L21uPjwvbXNxcnQ+PC9tYXRoPu4bDgwAAAAASUVORK5CYII=)
Find the values of a and b : ![fraction numerator 5 plus 3 square root of 2 over denominator 5 minus 3 square root of 2 end fraction equals a plus b square root of 2](data:image/png;base64,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)
Maths-General