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# What are exponents?

Power and scientific notation are often used in the laboratory so it is important to familiarise yourself with them.

The power (or exponent) is a number that indicates how many times another number (called the base) is multiplied by itself. For example, 2^{4} is read "two raised to the fourth power" and means that 2 is multiplied by itself 4 times.

Therefore, $ 2^4 = 2 \times 2 \times 2 \times 2 = 16 $

Or another, $ 4^5 = 4 \times 4 \times 4 \times 4 \times 4 = 1024 $

The number that is multiplied is called the base and the power to which the base is raised is the exponent. For example, in the expression 10^{3}, the base is 10 and the exponent is 3.

Alternatively, a negative exponent indicates that the reciprocal of the number (i.e. one divided by the number) should be multiplied times itself.

For example,

$$ \begin{align*} 1 \div 10^3 &= 10^{-3} \cr &= \frac{1}{10\times 10\times 10} \cr &= \frac{1}{10} \times \frac{1}{10} \times \frac{1}{10} \cr &= \frac{1}{1000} \cr &= 0.001 \end{align*} $$

When looking at exponents where the base is 10 (which is the majority of the time in science), there are two general rules to remember:

For numbers greater than 1:

- The exponent or power represents the number of zeros after the number and before the decimal point
- If the exponent or power is positive, the larger the positive exponent, the larger the number.

For example, 1 x 10^{4} = 10,000.0 (notice that there are 4 zeros before the decimal point).

For numbers less than 1:

- The exponent or power represents the number of places to the right of the decimal point including the first non-zero digit
- The exponent or power is negative

For example, 1 x 10^{-4} = 10^{-4} = 0.0001 (notice that it is 4 places to the right of the decimal place)

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