Use the digits in the year 2010 and the operations +, -, x, ÷, sqrt (square root), ^ (raise to a power), and ! (factorial) — along with parentheses, brackets, or other grouping symbols — to write expressions for the counting numbers 1 through 100.
All four digits must be used in each expression.
1. Only the digits 2, 0, 1, 0 may be used.
2. The decimal point may be used, as in .1, .02, etc.
3. Multi-digit numbers such as 20 or 102 may be used.
Please use the name of the subject so that teachers will know what kind of help is needed.
I will start you off:
100= 2^0 * 100
99=100-2^0
98=100-2
97=100-(2+1)
and you finish.
what is the answer for1/3+(2/5 multiplied by 25/12)
To write expressions for the counting numbers 1 through 100 using only the digits in the year 2010 and the given operations, we can go through each number and try to find a combination that satisfies the conditions. Here are some examples:
1. 1 = sqrt(sqrt((2 + 0)! + 1 + 0))
To get the square root of a number, we can use the sqrt function. The factorial (!) is also an operation that we can use to create different numbers.
2. 2 = sqrt(2 + 0 + 1 + 0)
Here we use the sqrt function to get the square root of the sum of all four digits.
3. 3 = (sqrt(2) + 0 + 1 + 0)!
We use the sqrt function to get the square root of 2, then add the other digits and apply the factorial (!).
4. 4 = sqrt(2 + 0 + 1 + 0)^((0+1)!)
Using the power (^) operation, we raise the sum of the digits to the power of the factorial of (0 + 1).
5. 5 = (2 + 0 + 1 + 0)/0.2
Here we divide the sum of the digits by 0.2, which is equivalent to multiplying by 5.
6. 6 = (2 + 0 + 1) * sqrt(0 + 0)
We add the first three digits and multiply the result by the square root of 0.
7. 7 = 2^0 + 1 - 0!
We raise 2 to the power of 0, add 1, and subtract the factorial of 0.
8. 8 = (2 + 0!) * (1 + 0)
We calculate the factorial of 0, add it to 2, and multiply the result by the sum of 1 and 0.
9. 9 = (2 * 0) + 1 + sqrt(0)
We multiply 2 by 0, add 1, and add the square root of 0.
10. 10 = (2 * 0 + 1 + 0)!
We multiply 2 by 0, add 1, add 0, and finally apply the factorial.
These are just a few examples, and there might be multiple ways to express each number. By combining the digits 2, 0, 1, 0 with the given operations, you can create expressions for all the counting numbers from 1 to 100.