13. Express \[$\frac{}{1000}\$\] As A Decimal.14. When I Multiply A Number By \[$\frac{3}{5}\$\], The Result Is 150. What Is The Number?15. Multiply 8.04 By 1.3 And Round Your Answer To The Nearest Tenth.

Converting Fractions to Decimals

In mathematics, converting fractions to decimals is an essential skill that helps us solve real-world problems. A fraction is a way of expressing a part of a whole as a ratio of two numbers. To convert a fraction to a decimal, we divide the numerator (the top number) by the denominator (the bottom number).

Example 1: Expressing a Fraction as a Decimal

Problem: Express $\frac{1}{1000}$ as a decimal.

Solution: To convert the fraction $\frac{1}{1000}$ to a decimal, we divide the numerator (1) by the denominator (1000).

$\frac{1}{1000} = 0.001$

Therefore, the decimal equivalent of $\frac{1}{1000}$ is 0.001.

Example 2: Expressing a Fraction as a Decimal

Problem: Express $\frac{3}{5}$ as a decimal.

Solution: To convert the fraction $\frac{3}{5}$ to a decimal, we divide the numerator (3) by the denominator (5).

$\frac{3}{5} = 0.6$

Therefore, the decimal equivalent of $\frac{3}{5}$ is 0.6.

Solving Real-World Problems

In addition to converting fractions to decimals, we can also use fractions to solve real-world problems. For example, if we know that a certain product is 3/5 of the total cost, we can use this information to calculate the total cost.

Example 3: Solving a Real-World Problem

Problem: When I multiply a number by $\frac{3}{5}$, the result is 150. What is the number?

Solution: To solve this problem, we can set up an equation using the given information. Let x be the number we are trying to find.

$\frac{3}{5}x = 150$

To solve for x, we can multiply both sides of the equation by 5/3.

$x = 150 \times \frac{5}{3}$

$x = 250$

Therefore, the number we are trying to find is 250.

Rounding Numbers

In addition to converting fractions to decimals and solving real-world problems, we can also use fractions to round numbers. For example, if we know that a certain number is 8.04, we can use this information to round the number to the nearest tenth.

Example 4: Rounding a Number

Problem: Multiply 8.04 by 1.3 and round your answer to the nearest tenth.

Solution: To solve this problem, we can multiply 8.04 by 1.3.

$8.04 \times 1.3 = 10.452$

To round this number to the nearest tenth, we can look at the hundredth place (the second digit after the decimal point). Since the hundredth place is 5, we can round the number up to 10.5.

Therefore, the result of multiplying 8.04 by 1.3 and rounding to the nearest tenth is 10.5.

Conclusion

Q: What is the difference between a fraction and a decimal?

A: A fraction is a way of expressing a part of a whole as a ratio of two numbers, while a decimal is a way of expressing a number as a sum of powers of 10.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, you can divide the numerator (the top number) by the denominator (the bottom number).

Q: What is the decimal equivalent of $\frac{1}{1000}$?

A: The decimal equivalent of $\frac{1}{1000}$ is 0.001.

Q: What is the decimal equivalent of $\frac{3}{5}$?

A: The decimal equivalent of $\frac{3}{5}$ is 0.6.

Q: How do I solve a real-world problem using fractions?

A: To solve a real-world problem using fractions, you can set up an equation using the given information and then solve for the unknown variable.

Q: What is the number that, when multiplied by $\frac{3}{5}$, gives 150?

A: The number that, when multiplied by $\frac{3}{5}$, gives 150 is 250.

Q: How do I round a number to the nearest tenth?

A: To round a number to the nearest tenth, you can look at the hundredth place (the second digit after the decimal point) and round up or down accordingly.

Q: What is the result of multiplying 8.04 by 1.3 and rounding to the nearest tenth?

A: The result of multiplying 8.04 by 1.3 and rounding to the nearest tenth is 10.5.

Q: Can I use fractions to solve problems involving percentages?

A: Yes, you can use fractions to solve problems involving percentages. For example, if you know that a certain product is 25% off, you can use a fraction to calculate the discount.

Q: How do I calculate the discount on a product that is 25% off?

A: To calculate the discount on a product that is 25% off, you can multiply the original price by the fraction $\frac{3}{4}$ (since 25% is equivalent to $\frac{1}{4}$).

Q: What is the formula for calculating the area of a rectangle?

A: The formula for calculating the area of a rectangle is $A = lw$, where $A$ is the area, $l$ is the length, and $w$ is the width.

Q: Can I use fractions to solve problems involving geometry?

A: Yes, you can use fractions to solve problems involving geometry. For example, if you know that a certain triangle has angles that add up to 180°, you can use a fraction to calculate the measure of each angle.

Q: How do I calculate the measure of each angle in a triangle that adds up to 180°?

A: To calculate the measure of each angle in a triangle that adds up to 180°, you can use the formula $m\angle A + m\angle B + m\angle C = 180°$, where $m\angle A$, $m\angle B$, and $m\angle C$ are the measures of each angle.

Conclusion

In conclusion, fractions are a powerful tool for solving real-world problems and can be used to convert decimals, solve equations, and calculate percentages and areas. By understanding how to use fractions, you can develop problem-solving skills that can be applied to a wide range of situations.