Which nonterminating decimal can be converted into a rational number?
0.818118111...
0.020304050...
0.010110111...
0.321321321... ***
George has a square sandbox in the backyard. The sandbox has an area of 160 square feet. To the nearest foot, what is the length of one side of the sandbox?
11 ft
12 ft ***
40 ft
80 ft
A number can be rational and irrational. True or false?
True, I think?
Thanks for helping me out!
1. You're correct, because the decimal repeats digits, it's considered rational.
2. I believe that's correct. It doesn't come out to 160ft^2, of course, but it's sure close at least.
3. This is false, actually. Rationals and Irrationals form their own separate, distinct categories regardless if both of them are still real numbers.
isnt it 40 cause the sandbox is a square so u divide 160 by 4 and get 40.
You're welcome! I'm here to help and add a little humor along the way. Let's tackle your questions one by one:
1. Which nonterminating decimal can be converted into a rational number? Well, there's a lot of decimals out there, but let's pick the one that already has a fancy rhythm to it – the one that goes 0.321321321... That sure sounds like a party in decimal form!
2. Ah, George and his sandbox conundrum. He has a square sandbox with an area of 160 square feet. To find the length of one side, we need to take the square root of the area. After some calculations, the length of one side is approximately 12 feet. So, it looks like George's sandbox is perfect for some fun!
3. Can a number be both rational and irrational? Well, that's like wearing a tuxedo with swim fins – a bit of a mixed message. Actually, it's false. A number can either be rational, which means it can be expressed as a fraction, or irrational, which means it cannot be expressed as a fraction. They're like two different species in the number world - "irrationalicus" and "fractionarius." They don't like to mingle.
I hope I could assist you with a chuckle or two! Feel free to ask me more questions – I'm here to entertain and enlighten!
You're welcome! Below are the step-by-step explanations for each of your questions:
Which nonterminating decimal can be converted into a rational number?
- A rational number can be expressed as the quotient of two integers. Therefore, any repeating or recurring decimal can be converted into a rational number. Among the options you provided, the nonterminating decimal 0.321321321... can be converted into a rational number.
George has a square sandbox in the backyard. The sandbox has an area of 160 square feet. To the nearest foot, what is the length of one side of the sandbox?
- To find the length of one side of a square, we need to take the square root of its area. Therefore, taking the square root of 160 square feet, we get:
√160 ≈ 12.6491106407
Rounding to the nearest foot, the length of one side of the sandbox is approximately 12 feet.
A number can be rational and irrational. True or false?
- False. A number cannot be both rational and irrational. A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a fraction and has a non-repeating, non-terminating decimal representation.
You're welcome! I'm here to help. Let's go through your questions one by one.
Which nonterminating decimal can be converted into a rational number?
To determine if a nonterminating decimal can be converted into a rational number, we need to see if the decimal pattern repeats. For example, the decimal 0.818118111... has a repeating pattern of "181." Since it repeats, we can convert it into a rational number. This means that 0.818118111... can be converted into a rational number.
George has a square sandbox in the backyard. The sandbox has an area of 160 square feet. To the nearest foot, what is the length of one side of the sandbox?
To find the length of one side of the sandbox, we need to take the square root of the area. The square root of 160 is approximately 12.65. However, we need to round to the nearest foot, so the length of one side of the sandbox is 12 feet.
A number can be rational and irrational. True or false?
False. By definition, a number can only be classified as either rational or irrational, but not both. A rational number is a number that can be expressed as a fraction or ratio of two integers, while an irrational number cannot be expressed as a fraction and has an infinite decimal expansion without any repeating pattern.
I hope this clarifies everything for you! Feel free to ask if you have any more questions.