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Chapter 1: Problem 609

Write each decimal as a fraction. $$ 0.52 $$

Short Answer

Expert verified
0.52 = \(\frac{13}{25}\).

Step by step solution

01

Identify the place value

Determine the place value of the last digit in the decimal. For 0.52, the last digit (2) is in the hundredths place.
02

Write as a fraction

Write the decimal as a fraction with the denominator as a power of 10 based on the place value. For 0.52, it is written as \(\frac{52}{100}\).
03

Simplify the fraction

Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 52 and 100 is 4. So, divide both the numerator and the denominator by 4: \[\frac{52 \div 4}{100 \div 4} = \frac{13}{25}\].

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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 when converting decimals to fractions. Every digit in a decimal number has a specific place value. For instance, in the decimal 0.52, the digit '5' is in the tenths place, and the digit '2' is in the hundredths place. This means that 0.52 is the same as 52 hundredths or \[\frac{52}{100}\].
To break it down further:
  • The first digit to the right of the decimal point is the tenths place.
  • The second digit to the right of the decimal point is the hundredths place.
Recognizing these positions helps in converting decimals to fractions accurately.
simplifying fractions
After converting a decimal to a fraction, the next important step is simplifying the fraction. Simplifying means reducing the fraction to its simplest form.
To do this:
  • Identify a common factor that both the numerator (top number) and the denominator (bottom number) share.
  • Divide both the numerator and the denominator by this common factor.
For example, we converted 0.52 to the fraction \[\frac{52}{100}\]. Upon finding the greatest common divisor (GCD) of 52 and 100, which is 4, we then divide both by 4, giving us the simplified fraction \[\frac{13}{25}\].
greatest common divisor (GCD)
The Greatest Common Divisor (GCD), also known as the Greatest Common Factor (GCF), plays an essential role in simplifying fractions. It is the largest number that divides both the numerator and the denominator without leaving a remainder.
Finding the GCD:
  • List out the factors of both the numerator and the denominator.
  • Identify the largest factor that both numbers share.
For 52 and 100:
- The factors of 52 are 1, 2, 4, 13, 26, and 52.
- The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
The largest common factor here is 4, which means the GCD is 4. Therefore, we use this GCD to simplify \[\frac{52}{100} \] to \[\frac{13}{25} \].

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Most popular questions from this chapter

Helen bought a 24-pound turkey for her family's Thanksgiving dinner and wants to know what time to put the turkey in to the oven. She wants to allow 20 minutes per pound cooking time. Calculate the length of time needed to roast the turkey: (a) First, by multiplying \(24 \cdot 20\) to find the total number of minutes and then multiplying the answer by \(\frac{1}{60}\) to convert minutes into hours. (b) Next, by multiplying \(24\left(20 \cdot \frac{1}{60}\right)\). (C) Which of the properties of real numbers says that your answers to parts (a), where you multiplied \((24 \cdot 20) \frac{1}{60}, \quad\) and \(\quad(b),\) where you multiplied \(24\left(20 \cdot \frac{1}{60}\right),\) should be equal?

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