Q: How to Convert a Number into Fraction

The direct answer: Express the number as a ratio of two integers (a fraction). For decimals, clear the decimal by multiplying by a power of 10; for repeating decimals use an algebraic subtraction trick; for mixed numbers convert to an improper fraction. Irrational numbers (like $\pi$ or $\sqrt2$) cannot be written exactly as fractions. Explanation & Steps 1) Whole numbers Any whole number $n$ is $n/1$. 2) Terminating decimals (finite decimal places) Count the number of decimal digits $d$. Multiply by $10^d$ to remove the decimal, then divide by $10^d$ and simplify. Example: Convert $2.75$. $2.75 \times 100 = 275$ so $2.75 = \dfrac{275}{100}$. Simplify by $\gcd(275,100)=25$: $$\dfrac{275}{100}=\dfrac{11}{4}.$$ 3) Repeating decimals (periodic) Let $x$ be the repeating decimal. Multiply $x$ by a power of 10 to align one full repeat, then by a larger power so subtraction eliminates the repeating part. Example: $x=0.\overline{36}=0.363636\ldots$ Multiply by $100$: $100x=36.3636\ldots$ Subtract: $100x-x=36.3636\ldots-0.3636\ldots$ So $99x=36$, hence $$x=\dfrac{36}{99}=\dfrac{4}{11}.$$ Example: $0.\overline{6}$ $x=0.\overline{6}$, $10x=6.\overline{6}$, subtract: $9x=6$ so $$x=\dfrac{6}{9}=\dfrac{2}{3}.$$ General method for a decimal with non-repeating part $a$ (length $m$) and repeating block $b$ (length $n$):$$x=\frac{\text{integer formed by }(a\text{ then }b)-\text{integer formed by }(a)}{10^{m+n}-10^{m}}.$$ 4) Mixed numbers Convert $W\ \frac{p}{q}$ to improper fraction:$$W+\frac{p}{q}=\frac{Wq+p}{q}.$$ Example: $2\ \frac{3}{5}=\frac{2\cdot5+3}{5}=\frac{13}{5}$. 5) Simplify using GCD Always divide numerator and denominator by their greatest common divisor. Important note Irrational numbers cannot be exactly written as fractions — you can only give rational approximations (e.g., $\pi\approx\dfrac{22}{7}$). If you have a particular number you want converted, tell me the number and I’ll convert it step-by-step.

Q: Fraction of a Decimal

I’m not sure what you mean — do you mean (A) convert a decimal to a fraction, (B) find a fraction of a decimal (like “3/4 of 0.8”), or (C) convert a fraction to a decimal? Please tell me which or give a specific number. Quick explanations and examples A — Convert a decimal to a fraction Example: $0.75$ Steps: $0.75=\frac{75}{100}$, simplify by $25$: $\frac{75}{100}=\frac{3}{4}$. B — Find a fraction of a decimal Example: "Find $\frac{3}{4}$ of $0.8$" Steps: $\frac{3}{4}\times0.8=\frac{3}{4}\times\frac{8}{10}=\frac{24}{40}=\frac{3}{5}=0.6$. C — Convert a fraction to a decimal Example: $\frac{3}{8}$ → divide $3\div8=0.375$, so $\frac{3}{8}=0.375$. Tell me which of A/B/C you want (or give the specific decimal/fraction) and I’ll show full step-by-step work.

Q: 67 inches to feet

The correct answer is: $5\frac{7}{12}\text{ ft}\ (5.583333\text{ ft, approx})$ Explanation We convert inches to feet using $1\text{ ft}=12\text{ in}$. Steps: Write the conversion: $$\text{feet}=\frac{67\text{ in}}{12\text{ in/ft}}$$ Divide to get a mixed number: $$\frac{67}{12}=5+\frac{7}{12}=5\frac{7}{12}\text{ ft}$$ Decimal approximation: $$5\frac{7}{12}=5+0.583333\ldots\approx5.583333\text{ ft}$$ Therefore, 67 inches = $5\frac{7}{12}\text{ ft}$, about $5.583333\text{ ft}$.

Q: 66cm to inches

The correct answer is: $25.98\text{ in}$ Explanation To convert centimeters to inches use $1\text{ in} = 2.54\text{ cm}$. Divide the length in centimeters by $2.54$ to get inches. Steps: Formula: $$\text{inches}=\frac{\text{cm}}{2.54}$$ Substitute: $$\text{inches}=\frac{66}{2.54}$$ Calculate: $$\frac{66}{2.54}=25.9842519685\ldots\approx25.98\text{ in}$$ Therefore, $66\text{ cm}\approx25.98\text{ in}$ (about $26.0\text{ in}$).

Question

How do you Convert a number to a Fraction

Accepted Answer

The short answer: To convert a number to a fraction, write it with an integer numerator and a power-of-10 denominator (for terminating decimals or percentages) or use the algebra method for repeating decimals, then simplify by dividing numerator and denominator by their greatest common divisor.

Explanation

1) Terminating decimals (e.g., 0.75, 2.5)
Steps:

Count decimal places. Multiply numerator and denominator by a power of 10 to remove the decimal.
Simplify the resulting fraction.

Examples:

$0.75 = \dfrac{75}{100} = \dfrac{3}{4}$ (divide top and bottom by 25).
$2.5 = \dfrac{25}{10} = \dfrac{5}{2}$ (or $2\frac{1}{2} = \dfrac{5}{2}$).

2) Repeating decimals (e.g., $0.\overline{3}$, $0.1\overline{6}$)
Use algebra:

Let $x = 0.\overline{3}$. Then $10x = 3.\overline{3}$. Subtract: $9x = 3$, so $x = \dfrac{1}{3}$.
For non‑repeating + repeating part (example $x=0.1\overline{6}$): nonrepeating length $m=1$, repeating length $n=1$.
Compute $10^{m+n}x - 10^m x = $ integer difference.
$100x = 16.\overline{6}$ and $10x = 1.\overline{6}$ so $90x = 15$, hence $x = \dfrac{15}{90} = \dfrac{1}{6}$.

General formula: if decimal has nonrepeating part a and repeating part b,$$x = \frac{	ext{(all digits up to end of first repeat)} - 	ext{(nonrepeating digits)}}{10^{m+n} - 10^m}.$$

3) Percentages
Replace % with division by 100, then simplify:

$45\% = \dfrac{45}{100} = \dfrac{9}{20}$.

4) Mixed numbers
Convert the fractional part and add to the integer, or convert whole number to fraction over 1:

$2.75 = \dfrac{275}{100} = \dfrac{11}{4}$.

5) Simplify by GCD
Always divide numerator and denominator by their greatest common divisor (GCD) to get the fraction in lowest terms.

Quick checklist

Terminating decimal: multiply by $10^{	ext{decimal places}}$, simplify.
Repeating decimal: use algebraic subtraction (multiply by $10^{m+n}$ and $10^m$, subtract), simplify.
Percent: put over 100, simplify.
Mixed: convert to improper fraction or separately convert integer + fraction.

If you want, give me a specific number (like 0.142857, 3.125, or 12.5%) and I’ll convert it step-by-step.