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# Fractional Multiplications – Unexpected Results Of Positive Numbers [Duplicate] Top 15 Favorites

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### Fractional multiplications – unexpected results of positive numbers [duplicate]

It is possible that the unexpected results you are experiencing with fractional multiplications of positive numbers are due to limitations in the precision of floating-point arithmetic. Floating-point arithmetic can only represent a finite subset of the real numbers, and rounding errors can occur when performing operations on numbers that are not precisely representable.

For example, consider the multiplication of 0.1 and 0.2:

``````0.1 * 0.2 = 0.02
``````

However, due to rounding errors, a computer may produce a slightly different result:

```python```>>> 0.1 * 0.2
0.020000000000000004
``````

This result is very close to the correct answer, but it is not exactly equal to it due to rounding errors. These errors can accumulate over multiple arithmetic operations, leading to increasingly inaccurate results.

To avoid these issues, it is important to use appropriate numerical methods and to be aware of the limitations of floating-point arithmetic. For example, you can use decimal arithmetic or arbitrary-precision arithmetic libraries to perform calculations with higher precision and accuracy.

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Multiplying Fractions – Positive Only

### What happens when you multiply a positive number by a positive number greater than 1?

When you multiply a positive number by a positive number greater than 1, the result will be a larger positive number than the original. This is because when you multiply by a number greater than 1, you are effectively adding that number to itself multiple times.

For example, if you multiply 5 by 2, you get 10. This is because 2 is being added to itself 5 times (2+2+2+2+2). Similarly, if you multiply 10 by 3, you get 30 because 3 is being added to itself 10 times (3+3+3+3+3+3+3+3+3+3).

In general, if you multiply a positive number x by a positive number y greater than 1, the result will be a larger positive number than x, and the exact value will be xy.

### What happens when you multiply a positive fraction to a negative fraction?

When you multiply a positive fraction by a negative fraction, the result is a negative fraction.

To understand why, we can use the following example:

Let’s say we want to multiply the positive fraction 1/4 by the negative fraction -2/3.

1/4 * (-2/3)

We can simplify this expression by multiplying the numerators together and multiplying the denominators together:

(1 * -2) / (4 * 3)

-2/12

We can simplify this fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

-2/12 = (-1 * 2) / (6 * 2) = -1/6

So the result of multiplying a positive fraction by a negative fraction is a negative fraction.

### What is the result of repeated multiplication?

The result of repeated multiplication is the product of the numbers that are being multiplied together multiple times.

For example, if we repeatedly multiply the number 2 by itself, we get:

• 2 x 2 = 4
• 4 x 2 = 8
• 8 x 2 = 16
• 16 x 2 = 32
• and so on.

The result of repeated multiplication in this case is an exponentially increasing sequence of numbers that are all multiples of 2.

Similarly, if we repeatedly multiply any two numbers together, we get a product that is the result of multiplying those numbers multiple times. The result of repeated multiplication depends on the numbers being multiplied and how many times they are being multiplied.

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