Question

Is 22.8 x 4.7 reasonable or not

Answer 1

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

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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)