Problem 610 Write each decimal as a fraction... [FREE SOLUTION]

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Chapter 1: Problem 610

Write each decimal as a fraction. $$ 0.78 $$

Short Answer

Expert verified

0.78 as a fraction is $ \frac{39}{50} $.

Step by step solution

Identify the Place Value

The decimal 0.78 means 78 hundredths because the digit 8 is in the hundredths place.

Write the Fraction

Write 0.78 as a fraction with 78 as the numerator and 100 as the denominator: $ \frac{78}{100} $

Simplify the Fraction

Simplify the fraction by finding the greatest common divisor (GCD) of 78 and 100, which is 2. Divide both the numerator and the denominator by their GCD: $ \frac{78 \div 2}{100 \div 2} = \frac{39}{50} $

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Key Concepts

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

place value

Understanding place value is essential when converting decimals to fractions. Place value refers to the position of a digit in a number, which determines its value. For example, in the decimal number 0.78, the 7 is in the tenths place, and the 8 is in the hundredths place. This means that 0.78 can be expressed as seventy-eight hundredths or \[ \frac{78}{100} \]. By identifying the place value of each digit, you can write the decimal as a fraction accurately. Each subsequent place in a decimal denotes a tenfold decrease in the digit鈥檚 value.

fraction simplification

Once you have converted a decimal to a fraction, the next step is to simplify the fraction to its simplest form. Simplifying a fraction means reducing it so that the numerator and the denominator are as small as possible while still maintaining the same value. For example, from the given problem, the fraction \[ \frac{78}{100} \] can be simplified. To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 78 and 100 is 2. Therefore, \[ \frac{78}{100} \] simplifies to \[ \frac{39}{50} \].

greatest common divisor (GCD)

Finding the greatest common divisor (GCD) is crucial for fraction simplification. The GCD of two numbers is the largest number that divides both of them without leaving a remainder. In the example of \[ \frac{78}{100} \], we determine the GCD by listing the factors of each number. The factors of 78 are 1, 2, 3, 6, 13, 26, 39, and 78. The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. The largest common factor is 2. Therefore, the GCD of 78 and 100 is 2. Dividing the numerator and the denominator by their GCD reduces the fraction to its simplest form \[ \frac{39}{50} \].

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91影视

Write each decimal as a fraction. $$ 0.78 $$

Short Answer

Step by step solution

Identify the Place Value

Write the Fraction

Simplify the Fraction

Key Concepts

place value

fraction simplification

greatest common divisor (GCD)

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