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Chapter 2: Problem 116

Convert the decimal to a fraction. $$0.48$$

Short Answer

Expert verified
The decimal 0.48 converted to a fraction is \(\frac{12}{25}\).

Step by step solution

01

Recognize the decimal place

The decimal number 0.48 is composed of two decimal places. The first digit after the decimal point represents tenths and the digit after that shows hundredths. So, the decimal number 0.48 can be read as 48 hundredths.
02

Convert to Fraction

Convert 0.48 into a fraction using the place value. Since 48 is in the hundredths place, express this as a fraction over 100 to become \(\frac{48}{100}\).
03

Simplify the Fraction

To simplify the fraction, find the greatest common divisor (GCD) for the numerator and the denominator i.e. 48 and 100. The GCD is 4. Next, divide the numerator and denominator by this number to simplify the fraction, resulting in \(\frac{48}{4}\)/ \(\frac{100}{4}\), which simplifies to \(\frac{12}{25}\).

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Key Concepts

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

Decimal Place Value
Understanding decimal place value is crucial for converting decimals to fractions. When you look at a decimal number like 0.48, each digit after the decimal point has a specific place value. The first digit represents tenths, which in this case is 4. The second digit represents hundredths, which is 8. Thus, 0.48 can be expressed as "48 hundredths". Visualizing the decimal in terms of money can make it even easier: think of 0.48 as $0.48 or 48 cents out of 100 cents in a dollar. Appreciating this conversion helps when you change the decimal to a fraction, as you now know this is equal to \(\frac{48}{100}\).
Simplifying Fractions
Simplifying fractions makes them easier to understand and use in operations. Here, the goal is to express \(\frac{48}{100}\) in its simplest form. To simplify a fraction, you divide both the numerator (the top number) and the denominator (the bottom number) by their Greatest Common Divisor (GCD). The GCD is the largest number that evenly divides both numbers.Follow these steps:
  • Identify the GCD of the numerator and denominator.
  • Divide both the numerator and denominator by this GCD.
Applying these steps to \(\frac{48}{100}\), we simplify to \(\frac{12}{25}\) by dividing by the GCD, which is 4.
Greatest Common Divisor
The Greatest Common Divisor (GCD) is an essential concept when simplifying fractions. It is the largest number that can divide two numbers without leaving a remainder. To find the GCD, begin by listing the factors of each number. For the numbers 48 and 100:
  • Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
  • Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
The largest common factor is 4, which is the GCD of 48 and 100. With this knowledge, you simplify \(\frac{48}{100}\) to \(\frac{12}{25}\) by dividing both the numerator and denominator by 4. Mastering the GCD allows you to effectively simplify fractions without guesswork.

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Most popular questions from this chapter

Find the force exerted on a falling object that has a mass of 4.25 kg. Use the formula \(F=m a,\) where \(F\) is the force exerted by gravity on a falling object, \(m\) is the mass of the object, and \(a\) is the acceleration due to gravity. The acceleration due to gravity is \(9.80 \mathrm{m} / \mathrm{s}^{2}\) (meters per second squared). The force is measured in newtons.

\(A\) standard deck of playing cards consists of 52 cards. a. What fractional part of a standard deck of cards is spades? b. What fractional part of a standard deck of cards is aces?

Divide and round to the nearest hundredth. Then check by estimating the quotient. $$421.093 \div 4.087$$

Place the correct symbol, \(<\) or \(>,\) between the two numbers. $$0.25 \quad \frac{13}{50}$$

Divide and round to the nearest hundredth. Then check by estimating the quotient. $$6.398 \div 5.5$$
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