What Is The Fractional Form Of

Your topic got cut off — "what is the fractional form of" is missing the actual number, decimal, percentage, or expression you want converted.

Tell me which one you mean and I'll write the full article. For example:

• a decimal like 0.375, 0.15, or 2.4
• a repeating decimal like 0.333... or 0.1666...
• a percentage like 45% or 12.5%
• a radical or root like √2 or 1/√3
• a ratio, mixed number, or algebraic expression

If you meant a general piece covering all of these — "how to convert decimals, percentages, and repeating decimals into fractional form" — just say so and I'll write that instead Worth keeping that in mind..

Because no specific number was supplied, the most useful continuation is a complete guide to converting the most common forms—terminating decimals, repeating decimals, and percentages—into fractional form.

Terminating Decimals

A terminating decimal ends after a finite number of digits. Still, to convert it, count the decimal places, use that count to determine the denominator (10, 100, 1000, etc. ), and then simplify.

Take 0.375. It has three decimal places, so write it as:

[ \frac{375}{1000} ]

Both numerator and denominator are divisible by 125:

[ \frac{3

Thus, 0.375 simplifies to (\frac{3}{8}).

Repeating Decimals

A repeating decimal contains a digit or block of digits that repeats infinitely. The standard technique is to set the decimal equal to a variable, multiply by a power of ten that moves the repeat to the left of the decimal point, then subtract the original equation to eliminate the repeating part.

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Example 1: (0.\overline{3}) (i.e., (0.333\ldots))

1. Let (x = 0.333\ldots)
2. Multiply by 10 (one digit repeats): (10x = 3.333\ldots)
3. Subtract the original equation:
   [ 10x - x = 3.333\ldots - 0.333\ldots \ 9x = 3 ]
4. Solve for (x): (x = \frac{3}{9} = \frac{1}{3}).

Example 2: (0.16\overline{6}) (i.e., (0.1666\ldots))

1. Let (x = 0.1666\ldots)
2. Multiply by 100 (two digits, the non‑repeating “16” and the repeating “6”): (100x = 16.666\ldots)
3. Multiply by 10 (one repeating digit): (10x = 1.666\ldots)
4. Subtract:
   [ 100x - 10x = 16.666\ldots - 1.666\ldots \ 90x = 15 ]
5. Solve: (x = \frac{15}{90} = \frac{1}{6}).

In each case, the fraction is obtained by reducing the resulting ratio to lowest terms It's one of those things that adds up. Nothing fancy..

Percentages

A percentage is simply a fraction with denominator 100. Converting a percent to a fraction follows two steps:

1. Write the percent as “value / 100”.
2. Reduce the fraction by dividing numerator and denominator by their greatest common divisor (GCD).

Example: (45%)

[ 45% = \frac{45}{100} = \frac{45 \div 5}{100 \