How to Order Fractions, Decimals, and Percentages

 

Understanding Fractions, Decimals, and Percentages

Each of these represents a part of a whole, just in different ways:

• Fraction: Represents a part of a whole, like $\frac{1}{2}$.
• Decimal: Shows part of a whole as a number after the decimal point, like $0.5$
• Percentage: A fraction out of $100$, often shown with a "$\%$" symbol, like $50\%$

 

Steps to Order Fractions, Decimals, and Percentages

To compare these numbers easily, convert everything to the same format, either all decimals or all percentages.

Method 1: Convert to Decimals

1. Convert each number to a decimal.

   • If you have a percentage, divide by $100$ to convert it to a decimal.
   • If you have a fraction, divide the numerator by the denominator.

2. Compare the decimal values.

3. Order from smallest to largest (or vice versa) based on their decimal values.

Example

Order $\frac{3}{4}, 0.8$ and $75\%$.

1. Convert each to a decimal:

   • $\frac{3}{4} = 0.75$
   • $0.8$ (already in decimal form
   • $75\% = 0.75$
2. Order the decimals: $0.75, 0.75, 0.8$
3. Write them in the original forms: $\frac{3}{4}, 75\%$ and $0.8$

So, the order from smallest to largest is $\frac{3}{4} = 75\%$, then $0.8$

 

Method 2: Convert to Percentages

1. Convert each number to a percentage.

   • If you have a decimal, multiply by $100$ to convert it to a percentage.
   • If you have a fraction, find an equivalent fraction out of $100$ or convert to a decimal and then to a percentage.
2. Compare the percentage values.

3. Order from smallest to largest (or vice versa) based on their percentage values.

 

Example

Order $0.6, \frac{4}{5}$ and $55\%$

1. Convert each to a percentage:
   • $0.6 \times 100 = 60\%$
   • $\frac{4}{5} = 0.8 \times 100 = 80\%$
   • $55\%$ (already in percentage form)
2. Order the percentages: $55\%,  60\%,  80\%$
3. Write them in the original forms:  \(55\%,  0.6}\) and $\frac{4}{5}$

So, the order from smallest to largest is \(55\%,  0.6}\) then $\frac{4}{5}$