We compute the product stepwise:
The multiplicand 0.023 has three significant figures; 1024 is exact (by definition, as a power of two). Therefore, the product should ideally retain three significant figures, yielding if rounded. However, 23.552 is the exact decimal result. 0.023 * 1024
If 0.023 arises from a measurement with uncertainty ( \pm 0.0005 ), the product’s range is: [ 0.0225 \times 1024 = 23.04, \quad 0.0235 \times 1024 = 24.064 ] Thus, the true value lies between 23.04 and 24.06, making 23.552 only one possible representation. We compute the product stepwise: The multiplicand 0
[ 0.023 \times 1024 = 0.023 \times (1000 + 24) ] [ = 0.023 \times 1000 + 0.023 \times 24 ] [ = 23 + 0.552 = 23.552 ] While mathematically straightforward
Alternatively, using fraction representation: [ 0.023 = \frac{23}{1000}, \quad \frac{23}{1000} \times 1024 = \frac{23 \times 1024}{1000} ] [ = \frac{23552}{1000} = 23.552 ]
Thus, the exact value is .
The expression ( 0.023 \times 1024 ) evaluates exactly to 23.552. While mathematically straightforward, its interpretation depends heavily on context—particularly the binary nature of 1024 and the precision of 0.023. In computing, it serves as a conversion between fractional and integer binary scales. In pure arithmetic, it illustrates decimal–binary interaction and significant figure considerations. Thus, even the simplest multiplications can reveal subtle conceptual depth.