How do you evaluate #\frac { 5\times 10^ {  3} } { 8\times 10^ {  2} }#?
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To evaluate (\frac{5 \times 10^{3}}{8 \times 10^{2}}), follow these steps:

Rewrite each number in scientific notation if necessary. In this case, both numbers are already in scientific notation.

Divide the numerical parts: ( \frac{5}{8} ).

Divide the exponential parts: ( 10^{3} \div 10^{2} ).

Apply the division rule for exponents: subtract the exponent in the denominator from the exponent in the numerator.

Simplify: ( \frac{5}{8} \times 10^{3(2)} ).

Combine exponents: ( \frac{5}{8} \times 10^{3+2} ).

Simplify the exponent: ( \frac{5}{8} \times 10^{1} ).

Convert the result back to standard notation if necessary: ( 0.625 \times 10^{1} ).

Finally, simplify by moving the decimal point one place to the left and changing the exponent: ( 0.0625 \times 10^0 ).

The final result is (0.0625 \times 10^0) or simply (0.0625).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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