Does doubling a number always make it larger?
This is a math question I have but I don’t know if the question is also including decimals because If it does then the answer would be no
If the number is positive, yes, doubling a number makes it larger.
However, if the number is negative, doubling it makes it "smaller".
Think of a number line.
If x is to the right of y on this line, then x is larger than y.
Now pick any positive number, say 3.5
double 3.5 = 2 * 3.5 = 7 and 7 would be to the right of 3.5, thus it is larger.
Now pick -6
2*(-6) = -12 and-12 is to the left of -6, thus it is smaller.
Forgot to mention zero.
Of course zero times any number is still zero, so there is no question about being larger or smaller.
In general, if you double a number, it will be larger than the original number. This holds true for whole numbers and most decimals as well. However, there are some instances where doubling a number does not make it larger. This occurs when the original number is negative or when the decimal number is less than 0.5. Would you like me to explain further?
To answer your question, let's first clarify what you mean by "doubling a number." If you're referring to multiplying any given number by 2, then yes, doubling a number will always make it larger if the number is a positive integer or a positive decimal.
To understand why doubling a number makes it larger in these cases, consider the concept of multiplication. When you multiply a number by 2, you are effectively adding the number to itself. Since the number is positive, adding it to itself will result in a larger number. For example:
1 multiplied by 2 is 2.
2 multiplied by 2 is 4.
3 multiplied by 2 is 6.
And so on.
However, if the number is negative, then doubling it will not always make it larger. In the case of negative numbers, doubling the number will result in a more negative value. For example:
-1 multiplied by 2 is -2.
-2 multiplied by 2 is -4.
-3 multiplied by 2 is -6.
And so on.
So, to specifically address your concern about decimals, the answer is still yes for positive decimals. For example:
0.5 multiplied by 2 is 1.
1.5 multiplied by 2 is 3.
2.5 multiplied by 2 is 5.
And so on.
In summary, doubling a number will always make it larger if the number is a positive integer or positive decimal. However, if the number is negative, doubling it will result in a more negative value.