I have no clue on this one. How would you solve:
us the (IN) key to express each number as a power. Then use the rules of logarithms to find the answer.
(45,332 x 10^5)(33,654 x 10^-4)
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93,153
(that is a fraction.)
please help.
To solve this problem, we will first convert the given numbers into a power of 10 using the logarithm rules. Let's break it down step by step:
Step 1: Expressing each number as a power of 10
For the numerator:
45,332 x 10^5 = 4.5332 x 10^4 (Divide by 10 once because 10^5 is equivalent to 10 times 10^4)
33,654 x 10^-4 = 3.3654 x 10^1 (Multiply by 10 four times because 10^-4 is equivalent to dividing by 10 four times)
For the denominator:
93,153 = 9.3153 x 10^4
So, the expression becomes:
(4.5332 x 10^4) x (3.3654 x 10^1)
------------------------
(9.3153 x 10^4)
Step 2: Simplifying the expression
To divide the fractions, we will subtract the exponent in the denominator from the exponent in the numerator.
(4.5332 x 10^4) x (3.3654 x 10^1) = 4.5332 x 3.3654 x 10^(4 + 1) = 15.26623828 x 10^5
(9.3153 x 10^4) = 9.3153 x 10^4
So, the expression becomes:
15.26623828 x 10^5
----------------
9.3153 x 10^4
Step 3: Divide the numbers
Divide the numerator by the denominator:
15.26623828 / 9.3153 = 1.638998971
Step 4: Simplify the powers of 10
When the same base is divided by the same base, the exponents are subtracted.
10^5 / 10^4 = 10^(5 - 4) = 10^1 = 10
So, the final answer is:
1.638998971 x 10
Therefore, the solution to the given expression is approximately 1.638998971 x 10 or 16.39.