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Question Convert \( 51 \% \) to a fraction in simplest form and a decimal. Answer Attempt 1 out of 2 ((L2) \begin{tabular}{l} Fraction: \\ Decimal (Edit the repeating and non-repeating part): \\ \hline\end{tabular}

Ask by Hart Rowe. in the United States
Jan 23,2025

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Tutor-Verified Answer

Answer

\( 51\% \) as a fraction in simplest form is \( \frac{51}{100} \) and as a decimal is 0.51.

Solution

Sure, let's convert \( 51\% \) to both a fraction in its simplest form and a decimal. ### Fraction: To convert a percentage to a fraction, you place the percentage value over 100 and simplify if possible. \[ 51\% = \frac{51}{100} \] **Simplification:** - The numerator is 51, and the denominator is 100. - The greatest common divisor (GCD) of 51 and 100 is 1. - Since the GCD is 1, the fraction is already in its simplest form. \[ \frac{51}{100} \] ### Decimal: To convert a percentage to a decimal, divide by 100. \[ 51\% = \frac{51}{100} = 0.51 \] **Details:** - **Non-repeating Part:** 0.51 - **Repeating Part:** None (since the decimal terminates) ### Summary | Conversion Type | Value | |-----------------|---------------| | **Fraction** | \(\dfrac{51}{100}\) | | **Decimal** | 0.51 |

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The Deep Dive

To convert \( 51 \% \) to a fraction, you start by understanding that percent means "per hundred." Thus, \( 51 \% \) can be written as \( \frac{51}{100} \). This fraction is already in its simplest form because there are no common factors between 51 and 100 other than 1. As for the decimal conversion, you divide the percentage by 100: \( 51 \div 100 = 0.51 \). So, \( 51 \% \) as a decimal is \( 0.51 \). For those curious about percentages, it may be interesting to note that converting from percentage to fraction is a skill that comes in handy in many real-world situations, like shopping (who doesn't love a good sale!). Understanding how to quickly convert can help you make decisions on discounts and prices without the calculator always at hand! If you're ever in doubt while working with fractions, just remember: always simplify your fraction to the lowest terms! A common mistake is to leave fractions unsimplified, which can lead to confusion down the road, especially when adding or comparing fractions later on. Always check for common factors to keep your work as neat as possible.

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