- Analyze the value of \(\frac{1}{100}\) as \(0.01\) and \(10^{-2}\).
- Evaluate each option provided:
- \(\frac{1}{100} = 0.01\) is a correct equality.
- \(\frac{1}{100} - 10^{-2} = 0\) is a correct equality equivalent to \(\frac{1}{100} = 10^{-2}\).
- Identify the true options: \(\boxed{\frac{1}{100} = 0.01, \frac{1}{100} - 10^{-2} = 0}\).
Explanation
- Evaluating the expression and its forms
To identify the true options among the given list, we first express the value of the fraction \(\frac{1}{100}\) in different forms.
Calculating the decimal form:
\[\frac{1}{100} = 0.01\]
Calculating the exponential form:
\[\frac{1}{100} = \frac{1}{10^2} = 10^{-2}\]
With these values established, we evaluate each of the provided statements individually to check for their mathematical validity.
- Testing the options for truth
Evaluating the options:
- \(\frac{1}{100} = 10^{-1}\): Since \(10^{-1} = 0.1\) and \(\frac{1}{100} = 0.01\), this is False.
- \(\frac{1}{100} = 0.001\): Since \(0.001 = \frac{1}{1000}\) and \(\frac{1}{100} = 0.01\), this is False.
- \(\frac{1}{100} = 1.100\): Since \(1.100 = 1.1\), this is False.
- \(\frac{1}{100} = 0.01\): This is True, as it correctly identifies the decimal value.
- \(\frac{1}{100} = 0.100\): Since \(0.100 = 0.1\), this is False.
- \(\frac{1}{100} - 10^{-3}\): This is an expression, not a complete equation; \(\frac{1}{100} - 10^{-3} = 0.01 - 0.001 = 0.009\).
- \(\frac{1}{100} = 0.1\): False.
- \(\frac{1}{100} - 10^{-2}\): As an equation \(\frac{1}{100} - 10^{-2} = 0\), this is True, because \(0.01 - 0.01 = 0\). This confirms the equality \(\frac{1}{100} = 10^{-2}\).
- Conclusion
Based on the evaluation, the two options that represent correct mathematical statements are \(\frac{1}{100} = 0.01\) and \(\frac{1}{100} - 10^{-2} = 0\). Thus, the two true options are the fourth and eighth ones. The final answer is \(\boxed{\frac{1}{100} = 0.01, \frac{1}{100} - 10^{-2} = 0}\).
Examples
In everyday life, understanding fractions and scientific notation is essential for measurements and conversions. For example, when dealing with currency, \(\frac{1}{100}\) of a dollar is exactly \(0.01\) dollars, or one cent. Recognizing that \(10^{-2}\) is equivalent to \(\frac{1}{100}\) helps in scientific fields, such as engineering or chemistry, where microscopic quantities are often represented using powers of 10 to ensure precision and clarity in calculations.