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Chapter 1: Problem 11

Convert the given decimal to a fraction. $$0.240$$

Short Answer

Expert verified
0.240 as a fraction is \(\frac{6}{25}\).

Step by step solution

01

Understand the Decimal

The decimal given is 0.240. This number has three digits after the decimal point.
02

Express as a Fraction over 1

Write the decimal as a fraction with 1 as the denominator: \( \frac{0.240}{1} \).
03

Multiply to Eliminate the Decimal

To eliminate the decimal places, multiply both the numerator and the denominator by 1000 (since there are three decimal places): \( \frac{0.240 \times 1000}{1 \times 1000} = \frac{240}{1000} \).
04

Simplify the Fraction

Simplify \( \frac{240}{1000} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 40: \( \frac{240 \div 40}{1000 \div 40} = \frac{6}{25} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Decimals to Fractions
Converting a decimal to a fraction is a fundamental skill in mathematics. It helps us understand numbers in different forms. When you see a decimal like 0.240, it can be expressed as a fraction. Here's how:

  • **Look at the Decimal:** Every decimal can be seen as a division of numbers. For 0.240, imagine it as 240 parts out of 1000. This is because there are three digits after the decimal point, meaning we're dealing with thousandths.
  • **Express the Decimal as a Fraction:** Start by writing the decimal as a fraction over 1. So 0.240 becomes \( \frac{0.240}{1} \).
  • **Eliminate the Decimal:** To remove the decimal, multiply both the numerator and the denominator by the same power of ten. For 0.240, since there are three decimal places, multiply by 1000: \( \frac{0.240 \times 1000}{1 \times 1000} = \frac{240}{1000} \).
By systematically converting the decimal into a fraction, you solidify your understanding of how these numerical representations are interrelated.
Simplifying Fractions
Simplifying fractions makes them easier to read and understand. It involves reducing the fraction to its smallest form. Here's a closer look at the process:

  • **Recognize the Fraction:** After converting a decimal, you need to simplify \( \frac{240}{1000} \).
  • **Identify the Greatest Common Divisor (GCD):** The GCD is the largest number that can evenly divide both the numerator and the denominator. For 240 and 1000, the GCD is 40.
  • **Divide to Simplify:** Divide both the numerator and the denominator by the GCD. So, \( \frac{240 \div 40}{1000 \div 40} = \frac{6}{25} \).
By simplifying, you reduce complexity and get \( \frac{6}{25} \), which is a neat and more understandable form of the number.
Mathematical Conversion
Mathematical conversion refers to changing numbers from one form to another. This might seem simple, but it's a powerful tool in mathematics and daily life.

  • **Understanding Conversion:** From decimals to fractions, or vice versa, conversion helps in comparing and evaluating numbers.
  • **Practical Application:** Know that some calculators or computer programs require input in specific formats, which involves converting numbers accordingly.
  • **Steps of Conversion in Practice:** Ensure you understand both decimal place values and fraction simplification to handle conversions smoothly and accurately.
Mastering conversions enhances problem-solving skills and deepens your numerical understanding, making math more intuitive and less daunting.

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Most popular questions from this chapter

Solve the inequality. Express your answer in both interval and set notations, and shade the solution on a number line. $$-11 x-9<-3 x+1$$

Solve each of the given equations for \(\mathrm{x}\). $$-48 x+95=0$$

Sketch the graph of the given interval. $$(-\infty, 2)$$

Use interval notation to describe the given set. Also, sketch the graph of the set on the real number line. $$\\{x: x \geq-1\( or \)x<3\\}$$

Solve each of the given equations for \(\mathrm{x}\). $$74 x-6=91$$
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