The number 0.5503 x 0.5503 x 0.5503 is close to 1/n, where n is an integer. What is the value of n that is closest to this number?

Question

GinnyAnswer · Answer

Calculate 0.550 3 3 , which is approximately 0.166647 . 
 Calculate 0.550 3 3 1 ​ , which is approximately 6.00069 . 
 Find the integer closest to 6.00069 , which is 6 . 
 The value of n that is closest to 0.550 3 3 1 ​ is 6 ​ . 
 
 Explanation 
 
 Understanding the Problem We are given the expression 0.5503 × 0.5503 × 0.5503 which is equal to 0.550 3 3 . We want to find an integer n such that 0.550 3 3 is close to n 1 ​ . This means we want to find the value of n that is closest to 0.550 3 3 1 ​ . 
 
 Calculating 0.5503 cubed First, we need to calculate 0.550 3 3 . The result of this calculation is approximately 0.166647 . 
 
 Calculating the reciprocal Next, we need to calculate 0.550 3 3 1 ​ , which is the same as 0.166647 1 ​ . The result of this calculation is approximately 6.00069 . 
 
 Finding the closest integer Now, we need to find the integer n that is closest to the value 6.00069 . The closest integer to 6.00069 is 6 . To verify this, we can check the absolute difference between 6.00069 and the integers around it. The absolute difference between 6.00069 and 5 is ∣6.00069 − 5∣ = 1.00069 . The absolute difference between 6.00069 and 6 is ∣6.00069 − 6∣ = 0.00069 . The absolute difference between 6.00069 and 7 is ∣6.00069 − 7∣ = 0.99931 . Since 0.00069 is the smallest difference, the closest integer is indeed 6 .

Examples 
 Imagine you are scaling down a photograph to fit a small frame. If the original photo's dimensions are approximately 0.55 x 0.55 x 0.55 meters, and you want to reduce it to about 1/n of its original size, finding the closest integer 'n' helps you determine the scaling factor for printing the miniature version. This concept is useful in graphic design, photography, and any field where scaling objects proportionally is necessary.

Anonymous · Answer

The value of n that is closest to 0.550 3 3 1 ​ is 6, calculated by finding the cube of 0.5503 and then determining its reciprocal. This results in approximately 6.00069, making 6 the nearest integer. Therefore, n = 6 . 
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The number 0.5503 x 0.5503 x 0.5503 is close to 1/n, where n is an integer. What is the value of n that is closest to this number?

Answer (2)

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