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 to turn Decimals into Fractions

Accepted Answer

Short answer: For a terminating decimal, write it as an integer over the appropriate power of 10 and simplify; for a repeating decimal use an algebraic trick (multiply and subtract) to get a rational fraction, then simplify.

Explanation & Steps

1) Terminating decimals (finite number of digits)
Steps:

Count how many digits are after the decimal point (call it $n$).
Multiply numerator and denominator so the decimal becomes an integer: put the digits as the numerator and $10^n$ as the denominator.
Simplify the fraction by dividing by the greatest common divisor (GCD).

Examples:

$0.75$ → digits after decimal $n=2$, numerator $75$, denominator $10^2=100$:

$$\frac{75}{100}=\frac{3}{4}$$

$0.2$ → $ \frac{2}{10}=\frac{1}{5}$
$1.25$ → separate whole part or convert directly: $1.25=\frac{125}{100}=\frac{5}{4}=1\frac{1}{4}$

2) Repeating decimals
Let $x$ be the decimal. If it has a repeating block of length $r$ and possibly a non-repeating part of length $n$ after the decimal:

Multiply $x$ by $10^{n+r}$ and also by $10^n$.
Subtract the two equations to cancel the repeating part.
Solve for $x$ and simplify.

General formula: If $x=0.a_1a_2\ldots a_n\overline{b_1\ldots b_r}$ (non-repeating $a$ length $n$, repeating $b$ length $r$),
$$x=\frac{\text{integer formed by }a_1..a_n b_1..b_r – \text{integer formed by }a_1..a_n}{10^{n+r}-10^n}.$$

Examples:

$0.\overline{3}$: let $x=0.\overline{3}$. Then $10x=3.\overline{3}$. Subtract:

$$10x-x=3\implies 9x=3\implies x=\frac{1}{3}.$$

$0.16\overline{7}$: non-repeating $=16$ ($n=2$), repeating $=7$ ($r=1$). Let $x=0.167777\ldots$.

Multiply: $10^{3}x=1000x=167.777\ldots$ and $10^{2}x=100x=16.777\ldots$.  Subtract: $900x=151\Rightarrow x=\frac{151}{900}$ (simplify if possible).

3) Negative decimals and mixed numbers

If the decimal is negative, put a minus sign: $-0.75=-\frac{3}{4}$.
For numbers >1, either convert whole+fraction separately (e.g., $2.05=2+\frac{5}{100}=2+\frac{1}{20}=2\frac{1}{20}$) or convert full decimal then simplify.

Tips

Always simplify the final fraction by dividing numerator and denominator by their GCD.
For long repeating patterns, use the general formula above.
If unsure how to simplify, use the Euclidean algorithm to find the GCD.

If you want, give me a specific decimal and I’ll convert it step-by-step.