1.66666666667 as a fraction in simplest form

1.66666666667 is a repeating decimal (1.666...). To convert it to a fraction:

1. Let \(x = 1.666...\)
2. Multiply both sides by 10: \(10x = 16.666...\)
3. Subtract the original equation from this: \(10x - x = 16.666... - 1.666...\)
4. Simplify: \(9x = 15\)
5. Solve for \(x\): \(x = \frac { 15} { 9} = \frac { 5} { 3} \)

Supplemental Knowledge

Converting repeating decimals to fractions is a useful mathematical skill. The decimal 1.66666666667 can be represented as \(1.\overline { 6} \), where the digit 6 repeats indefinitely. To convert this repeating decimal into a fraction, follow these steps:

1. \(\text { Let \(x\) be the repeating decimal: } \)
   \(x = 1.\overline { 6} \)
2. Multiply both sides by 10 to shift the decimal point:
   \(10x = 16.\overline { 6} \)
3. Subtract the original equation from this new equation to eliminate the repeating part:
   \(10x - x = 16.\overline { 6} - 1.\overline { 6} \)
   \(9x = 15\)
4. \(\text { Solve for \(x\): } \)
   \(x = \frac { 15} { 9} \)
5. Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD), which is 3:
   \(x = \frac { 15 ÷ 3} { 9 ÷ 3} = \frac { 5} { 3} \)

Thus, the simplest form of the fraction representing the repeating decimal \(1.\overline { 6} \) is \(5/3\).

Everyday Examples

Knowing how to convert repeating decimals to fractions can prove extremely useful when performing financial calculations, measuring food ingredients for recipes or programming with precise numerical data.
Imagine this: while cooking, you need to measure out ingredients accurately. If a recipe calls for amounts that result in repeating decimals when converted from cups to tablespoons, knowing how to express these measurements as fractions makes measuring accurately much simpler without resorting to approximations methods.

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