Evaluate 10^-3
Understand the Problem
The question is asking us to evaluate the expression 10 to the power of -3. This is a basic math problem that requires understanding of exponents.
Answer
$10^{-3} = 0.001$
Answer for screen readers
$10^{-3} = 0.001$
Steps to Solve
- Express the negative exponent as a fraction
A negative exponent means we take the reciprocal of the base raised to the positive exponent.
$10^{-3} = \frac{1}{10^3}$
- Evaluate the positive exponent
Calculate $10^3$, which means $10 \times 10 \times 10$.
$10^3 = 10 \times 10 \times 10 = 1000$
- Substitute the value back into the fraction
Replace $10^3$ with $1000$ in the fraction.
$\frac{1}{10^3} = \frac{1}{1000}$
- Convert the fraction to a decimal
Divide 1 by 1000 to get the decimal equivalent.
$\frac{1}{1000} = 0.001$
$10^{-3} = 0.001$
More Information
$10^{-3}$ is equivalent to one-thousandth. It's a common way to express very small numbers in a more compact form.
Tips
A common mistake is to think that a negative exponent makes the number negative. Instead, it represents the reciprocal of the number raised to the positive exponent. For example, $10^{-3}$ is not $-1000$ or $-0.001$, but rather $1/1000 = 0.001$.
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