Is 10^-3 = 0.001?
Understand the Problem
The question shows that 10 to the power of -3 equals 0.001. It likely intends to exemplify the concept of negative exponents and their relation to decimal representation.
Answer
$10^{-3} = 0.001$
Answer for screen readers
$10^{-3} = 0.001$
Steps to Solve
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Understand the negative exponent A negative exponent means taking the reciprocal of the base raised to the positive exponent. $10^{-3}$ is the same as $\frac{1}{10^3}$.
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Calculate the positive exponent Calculate $10^3$, which means $10 \cdot 10 \cdot 10 = 1000$.
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Calculate the reciprocal Now we have $\frac{1}{1000}$.
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Convert to decimal Converting $\frac{1}{1000}$ to a decimal gives $0.001$.
$10^{-3} = 0.001$
More Information
The expression $10^{-3}$ is indeed equal to $0.001$. This demonstrates the relationship between negative exponents and decimal places. Each decrease of 1 in the exponent increases the number of zeros after the decimal point by one.
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 $-10^3 = -1000$, but rather $\frac{1}{10^3} = \frac{1}{1000} = 0.001$.
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