To express $0.942$ as a fraction using equations, here’s a step-by-step solution based on the information in the image.

Solution Steps:

1. Set up an equation: Let $x = 0.942$.

2. Shift the decimal point to create similar terms: Multiply both sides by $10$, $100$, and $1000$ sequentially to shift the decimal point:

   • $10x = 9.42$
   • $100x = 94.2$
   • $1000x = 942.42$

3. Form an equation to eliminate the repeating decimal: Subtract the equation with $10x$ from the equation with $1000x$ to eliminate the decimal part. $1000x - 10x = 942.42 - 9.42$ Simplifying, we get: $990x = 933$

4. Solve for $x$: Divide both sides by $990$: $x = \frac{933}{990}$

5. Simplify the fraction: To simplify $\frac{933}{990}$, we find the greatest common divisor (GCD) of $933$ and $990$, which is $3$: $x = \frac{933 \div 3}{990 \div 3} = \frac{311}{330}$

Thus, $0.942$ as a fraction is $\frac{311}{330}$.

Would you like more details, or do you have any questions?

Here are some related questions:

1. What if we want to express a repeating decimal as a fraction?
2. How do we handle non-terminating decimals differently from terminating decimals?
3. What methods can be used to simplify fractions beyond finding the GCD?
4. How can multiplying by larger powers of 10 help in converting decimals to fractions?
5. Why does subtracting similar equations help in removing decimal parts?

Tip: When converting a decimal to a fraction, use powers of 10 to shift the decimal point, making it easier to form an equation for elimination.