Question

Convert the decimal 2.123(23) into a rational number in its standard form.

Answer 1

To convert 2.123(23) into a rational number in standard form, multiply both sides by 100, subtract the original equation from the new equation, and then finally simplify and divide to find the answer.

Step-by-step explanation:

To convert the decimal 2.123(23) into a rational number in its standard form, we need to express it as a fraction.

Let x = 2.123(23).

Multiply both sides of the equation by 100 to eliminate the repeating decimal: 100x = 212.323(23).

Subtract the original equation from the new equation: 100x - x = 212.323(23) - 2.123(23).

Simplify to get 99x = 210.2.

Divide both sides of the equation by 99: x = 210.2/99.

This is the rational number in its standard form.

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