Answer:
To write a number where 3 is worth 1/10 as much as 2 is worth 10 times, we need to assign values to each digit based on the given conditions.
1. Assigning values to digits:
- Let's assume the number has three digits: ABC.
- According to the given condition, the value of 2 should be 10 times greater than the value of 3. So, we can assign the value of 3 as X and the value of 2 as 10X.
2. Writing the number:
- Since the value of 3 is worth 1/10 as much as 2, we can write the number as 10X + X + X/10.
- Simplifying this expression, we get 10X + X + X/10 = 10X + 11X/10 = (100X + 11X)/10 = (111X)/10.
3. Finding a value for X:
- To satisfy the condition, X needs to be a non-zero value that satisfies the equation 3 = X/10 * 2 * 10.
- Solving this equation, we get X = 15.
4. Writing the final number:
- Substituting X = 15 into the expression (111X)/10, we get (111 * 15)/10 = 166.5.
Therefore, the number that satisfies the condition where 3 is worth 1/10 as much as 2 is worth 10 times is 166.5.
Explanation:
To write a number where 3 is worth 1/10 as much as 2 is worth 10 times, we need to assign values to each digit based on the given conditions.
1. Assigning values to digits:
- Let's assume the number has three digits: ABC.
- According to the given condition, the value of 2 should be 10 times greater than the value of 3. So, we can assign the value of 3 as X and the value of 2 as 10X.
2. Writing the number:
- Since the value of 3 is worth 1/10 as much as 2, we can write the number as 10X + X + X/10.
- Simplifying this expression, we get 10X + X + X/10 = 10X + 11X/10 = (100X + 11X)/10 = (111X)/10.
3. Finding a value for X:
- To satisfy the condition, X needs to be a non-zero value that satisfies the equation 3 = X/10 * 2 * 10.
- Solving this equation, we get X = 15.
4. Writing the final number:
- Substituting X = 15 into the expression (111X)/10, we get (111 * 15)/10 = 166.5.
Therefore, the number that satisfies the condition where 3 is worth 1/10 as much as 2 is worth 10 times is 166.5.