i am a three-digit decimal number. my thousandths is twice my tenths and my hundredths is the difference of my thousandths and tenths. what numbers am i
Let's say the number is written 0.ABC
C = 2A
B = C-A
That is only two equations in three unknowns. There could be more than one answer. A, B and C must be integers.
B = 2A - A = A
The number could be 0.112, 0.224, 0.336 or 0.448
If you say that B = A - C, there could be even more answers.
To find the number, let's use the given information and break down the different decimal places:
1. The thousandths place is twice the tenths place.
2. The hundredths place is the difference between the thousandths and tenths places.
Let's represent the number in the following format: abc, where a is the digit in the hundreds place, b is the digit in the tens place, and c is the digit in the units place.
Based on the given information, we know the following equations:
c = 2b (Equation 1)
b = a - c (Equation 2)
Now, let's substitute Equation 1 into Equation 2:
b = a - (2b)
b = a - 2b
Simplifying the equation:
b + 2b = a
3b = a
Since both sides of the equation are equal, we can iterate through possible values of b and find corresponding values for a and c that satisfy the equations.
Since the number is a three-digit decimal number, the possible values for a, b, and c range from 0 to 9.
Let's go through the possible values of b and find the corresponding values for a and c:
For b = 1, we have:
3(1) = a
a = 3
c = 2(1) = 2
Therefore, one possible number is 312.
For b = 2, we have:
3(2) = a
a = 6
c = 2(2) = 4
Therefore, another possible number is 624.
Through this process, we can find other combinations of a, b, and c, but these are the two possible answers based on the given conditions:
1. The number 312.
2. The number 624.