Question

Is 22.8 x 4.7 reasonable or not

Answer 1

Sure, the result of multiplying 22.8 by 4.7 is indeed reasonable. The result of multiplication is a fundamental arithmetic operation, and it's straightforward to perform on these two numbers. It does not depend on the nature of the numbers.

To confirm this, we simply multiply the two given numbers together.

First, we take the first number, which is 22.8.

Next, we multiply it by the second number, which is 4.7.

The result of this multiplication is a number.

The final step is to check if this result is a reasonable number or not. In mathematics, a reasonable result for this type of operation would typically be either an integer or a floating point number, which is a way of representing numbers that are not whole numbers.

In our case, the result of the multiplication is indeed a tangible number, so it is reasonable.

So, yes, the multiplication of 22.8 by 4.7 is reasonable.

Answer 2

For estimating purposes, you generally like to work with 1 significant digit, sometimes 2. The idea is to get a number "in the ballpark", sometimes along with an idea of whether that number is too high or too low. (The error estimate, too, is often approximated by 1 significant digit.)

22.8 × 4.7 ≈ 20 × 5 = 100

If you wanted a slightly more satisfying estimate, you could use

.. 23 × 5 = 115

_____

The actual value 4.7 is 0.3/5 = 6% lower than the value we're using in our computation. The actual value 22.8 = 2.8/10 = 14% higher than the value we're using for estimating. Hence the estimate of 100 may be 14%-6% = 8% lower than the actual value. (You can only add percentages like this when they are "small", so even this error estimate is in error.) That is, you exepect the actual value to be nearer 108. (22.8×4.7 is actually 107.16)