Problem 612 Write each decimal as a fraction... [FREE SOLUTION]

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Chapter 1: Problem 612

Write each decimal as a fraction. $$ 1.35 $$

Short Answer

Expert verified

$ \frac{27}{20} $

Step by step solution

- Identify the decimal

The decimal given is 1.35.

- Express the decimal as a fraction

Write 1.35 as a fraction. Since there are two digits after the decimal point, it can be written as $ \frac{135}{100} $.

- Simplify the fraction

Simplify $ \frac{135}{100} $ by finding the greatest common divisor (GCD) of 135 and 100. The GCD of 135 and 100 is 5. Thus, $ \frac{135}{100} $ simplifies to $ \frac{135 \div 5}{100 \div 5} = \frac{27}{20} $.

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Key Concepts

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

Simplifying Fractions

When we convert a decimal to a fraction, we often need to simplify the result to its lowest terms. This makes the fraction easier to understand and work with. Simplifying a fraction involves finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by this number.

For example, if we have the fraction $ \frac{135}{100} $, we can simplify it by finding the GCD of 135 and 100, which is 5. We then divide both the numerator and the denominator by 5:
\[ \frac{135 \div 5}{100 \div 5} = \frac{27}{20} \]
This fraction is now in its simplest form.

Greatest Common Divisor

The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator of a fraction without leaving a remainder. Finding the GCD is crucial for simplifying fractions.

To find the GCD of two numbers, you can use the Euclidean algorithm, which involves the following steps:

Divide the larger number by the smaller number
Take the remainder and divide it by the previous smaller number
Repeat until the remainder is zero
The last non-zero remainder is the GCD

For example, to find the GCD of 135 and 100:

135 divided by 100 is 1 with a remainder of 35
100 divided by 35 is 2 with a remainder of 30
35 divided by 30 is 1 with a remainder of 5
30 divided by 5 is 6 with no remainder
Thus, the GCD of 135 and 100 is 5

Place Value

Understanding place value is essential for converting decimals to fractions. Place value signifies the value of a digit based on its position in a number. Each position represents a power of 10.

For instance, in the decimal 1.35:

The '1' is in the units place (10^0)
The '3' is in the tenths place (10^-1)
The '5' is in the hundredths place (10^-2)

This means 1.35 can be written as 1 + 0.3 + 0.05. Since 0.3 is three-tenths and 0.05 is five-hundredths, combining these gives us a fraction representation. Placing the entire number over the appropriate power of 10 gives:
\[ \frac{135}{100} \]
This helps us accurately convert and understand decimal numbers in fractional form.

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91影视

Write each decimal as a fraction. $$ 1.35 $$

Short Answer

Step by step solution

- Identify the decimal

- Express the decimal as a fraction

- Simplify the fraction

Key Concepts

Simplifying Fractions

Greatest Common Divisor

Place Value

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