Fraction, Decimal, and Percent Match

1) Identify the three forms

A fraction, a decimal, and a percent can represent the same value in different ways. Your job is to match equivalent forms exactly, then give the simplest version when possible.

2) Convert carefully

Use one form to move to another:

• Fraction → decimal: divide the numerator by the denominator.
• Decimal → percent: multiply by 100 and add %.
• Percent → decimal: divide by 100.
• Percent → fraction: write it over 100 and simplify.
• Decimal → fraction: write the decimal as a fraction based on place value, then simplify.

3) Simplify the fraction

If the answer is a fraction, reduce it fully by dividing the numerator and denominator by their greatest common factor. A simplified fraction shows the same value with the smallest whole-number terms.

4) Check the match

A quick check is to convert your answer back into another form. The values should agree exactly. For example, the decimal and percent should line up by moving the decimal point two places.

5) Be exact

Do not round unless the exercise specifically says to. For matching problems, exactness matters:

• use terminating decimals when they are exact,
• write percents with the percent sign,
• simplify fractions completely.