Correct Answer: A

Rationale: To convert a decimal to a fraction, you can write the decimal as a fraction with the decimal part as the numerator and a power of 10 as the denominator. In this case, 0.75 can be written as 75/100. Simplifying this fraction by dividing both the numerator and denominator by 25 gives you 3/4. Therefore, the correct answer is A. Choice B (7/10), Choice C (15/20), and Choice D (1/2) are incorrect because they do not represent the correct conversion of 0.75 into a fraction.

Correct Answer: B

Rationale: The correct answer is B: 0.1 cm. One millimeter is equal to 0.1 centimeters, not 1/100th cm as mentioned in choice A. Choice C, 1 cm, is incorrect as a millimeter is smaller than a centimeter. Choice D, 10 cm, is incorrect as it incorrectly magnifies the conversion, making a millimeter larger than a centimeter. Therefore, the accurate conversion is that one millimeter equals 0.1 centimeters.

Correct Answer: A

Rationale: The mnemonic 'King Hector Died By Drinking Chocolate Milk' aids in recalling metric prefixes in order: kilo-, hecto-, deca-, base (meter, liter, gram), deci-, centi-, milli-. Choice B does not provide a relevant mnemonic for metric conversions. Choices C and D do not offer a helpful phrase for remembering metric prefixes, making them incorrect.

Correct Answer: B

Rationale: A balance scale is specifically designed to measure the mass of an object in grams or kilograms. It works based on the principle of balancing the unknown mass against a known mass. A thermometer is used to measure temperature, not mass, so choice A is incorrect. Choice C, 'scale,' is a bit vague and can refer to different types of scales, but a balance scale is the specific instrument used for measuring mass. Choice D, 'caliper,' is used for measuring dimensions such as length, width, or thickness, not mass.

Correct Answer: B

Rationale: To convert meters to kilometers, the conversion factor is 1 kilometer = 1,000 meters. Therefore, to find how many kilometers are in 1,000 meters, you divide 1,000 by 1,000, which equals 1 kilometer. Choice A (0.1 km), Choice C (10 km), and Choice D (0.01 km) are incorrect because they do not correctly represent the conversion of 1,000 meters to kilometers.