Standart şəkildə yazılışın tərtibi
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23. a, b və c bir-birindən fərqli ədədlər olarsa, standart şəkildə yazılmış $a \cdot 10^b$, $c \cdot 10^a$ və $b \cdot 10^c$ ədədlərinin hasili standart şəkildə yazılanda tərtibinin ən böyük qiymətində qiymətli hissəsi $d$ olarsa, $(-d)$ ədədinin tam hissəsini tapın. A) -4 B) -7 C) -8 D) -5 E) -6
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Hi Rehman, let's solve this problem involving numbers in standard form together.
Solving the Product in Standard Form
We are given three numbers in standard form: a times 10 to the power of b, c times 10 to the power of a, and b times 10 to the power of c.
Let's multiply these together. The product P is the product of the mantissas times 10 raised to the sum of the exponents.
In standard form, the mantissa m must satisfy 1 is less than or equal to m and m is less than 10. To maximize the exponent, we should choose the largest distinct digits available, which are 9, 8, and 7.
Assume \{a, b, c\} = \{9, 8, 7\}
Calculating the product of the mantissas gives us 504. So, P equals 504 times 10 to the power of 24.
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