Decimal to Fraction Conversion

Oct 13, 2025 by recoveryshake.com 59 views

1. Fraction Equivalent to 0.4

To find the fraction equivalent to 0.4, we need to convert the decimal to a fraction. We can do this by dividing the decimal by 1 and expressing it as a fraction.

Decimal to Fraction Conversion

The decimal 0.4 can be written as 4/10 or 2/5. Therefore, the fraction equivalent to 0.4 is 2/5.

2. Rectangle Diagonals

The length of the diagonal of a rectangle is given as 181 inches. We need to find the dimensions of the rectangle.

Rectangle Diagonals Formula

The formula for the diagonal of a rectangle is:

d = √(l² + w²)

where d is the diagonal, l is the length, and w is the width.

We are given the diagonal (d = 181 inches), but we need to find the length and width. Let's assume the length is l and the width is w.

3. Solving for Length and Width

We can substitute the given diagonal into the formula and solve for l and w.

181 = √(l² + w²)

To solve for l and w, we need to square both sides of the equation.

32441 = l² + w²

Now, we need to find two numbers whose sum is 32441 and whose product is a perfect square.

Perfect Square Numbers

After some trial and error, we find that 169² + 160² = 32441. Therefore, the length (l) is 169 and the width (w) is 160.

4. Conclusion

In conclusion, the fraction equivalent to 0.4 is 2/5, and the dimensions of the rectangle with a diagonal of 181 inches are 169 inches (length) and 160 inches (width).

Discussion

What other methods can be used to find the fraction equivalent to 0.4?
How can we use the formula for the diagonal of a rectangle to find the dimensions of other shapes?
What are some real-world applications of the formula for the diagonal of a rectangle?

Additional Problems

Find the fraction equivalent to 0.75.
Find the dimensions of a rectangle with a diagonal of 250 inches.
Find the area of a rectangle with a length of 200 inches and a width of 150 inches.

References

Q1: What is the fraction equivalent to 0.4?

A1: The fraction equivalent to 0.4 is 2/5. We can convert the decimal to a fraction by dividing the decimal by 1 and expressing it as a fraction.

Q2: How can we use the formula for the diagonal of a rectangle to find the dimensions of other shapes?

A2: The formula for the diagonal of a rectangle is:

d = √(l² + w²)

where d is the diagonal, l is the length, and w is the width. We can use this formula to find the dimensions of other shapes, such as triangles and trapezoids, by substituting the given diagonal and solving for the length and width.

Q3: What are some real-world applications of the formula for the diagonal of a rectangle?

A3: The formula for the diagonal of a rectangle has many real-world applications, such as:

Architecture: Architects use the formula to design buildings and ensure that the diagonal of a room or hallway is within a certain range.
Interior Design: Interior designers use the formula to determine the optimal placement of furniture and fixtures in a room.
Engineering: Engineers use the formula to design and build structures, such as bridges and buildings.

Q4: How can we find the fraction equivalent to a decimal?

A4: We can find the fraction equivalent to a decimal by dividing the decimal by 1 and expressing it as a fraction. For example, to find the fraction equivalent to 0.75, we can divide 0.75 by 1 and express it as a fraction: 3/4.

Q5: What is the formula for the diagonal of a rectangle?

A5: The formula for the diagonal of a rectangle is:

d = √(l² + w²)

where d is the diagonal, l is the length, and w is the width.

Q6: How can we use the formula for the diagonal of a rectangle to find the area of a rectangle?

A6: We can use the formula for the diagonal of a rectangle to find the area of a rectangle by first finding the length and width of the rectangle, and then using the formula for the area of a rectangle:

A = l × w

where A is the area, l is the length, and w is the width.

Q7: What are some common mistakes to avoid when using the formula for the diagonal of a rectangle?

A7: Some common mistakes to avoid when using the formula for the diagonal of a rectangle include:

Rounding errors: Make sure to round your answers to the correct number of decimal places.
Sign errors: Make sure to use the correct sign for the diagonal (positive or negative).
Unit errors: Make sure to use the correct units for the length and width (e.g. inches, feet, meters).

Q8: How can we use the formula for the diagonal of a rectangle to find the perimeter of a rectangle?

A8: We can use the formula for the diagonal of a rectangle to find the perimeter of a rectangle by first finding the length and width of the rectangle, and then using the formula for the perimeter of a rectangle:

P = 2(l + w)

where P is the perimeter, l is the length, and w is the width.

Q9: What are some real-world applications of the formula for the perimeter of a rectangle?

A9: The formula for the perimeter of a rectangle has many real-world applications, such as:

Construction: Builders use the formula to determine the amount of materials needed for a project.
Landscaping: Landscapers use the formula to determine the amount of materials needed for a project.
Furniture design: Furniture designers use the formula to determine the optimal size and shape of a piece of furniture.

Q10: How can we use the formula for the diagonal of a rectangle to find the volume of a rectangular prism?

A10: We can use the formula for the diagonal of a rectangle to find the volume of a rectangular prism by first finding the length, width, and height of the prism, and then using the formula for the volume of a rectangular prism:

V = l × w × h

where V is the volume, l is the length, w is the width, and h is the height.

Discussion

What other methods can be used to find the fraction equivalent to a decimal?
How can we use the formula for the diagonal of a rectangle to find the dimensions of other shapes?
What are some real-world applications of the formula for the diagonal of a rectangle?

Additional Problems

Find the fraction equivalent to 0.75.
Find the dimensions of a rectangle with a diagonal of 250 inches.
Find the area of a rectangle with a length of 200 inches and a width of 150 inches.