Problem 608 Write each decimal as a fraction... [FREE SOLUTION]

Chapter 1: Problem 608

Write each decimal as a fraction. $$ 0.19 $$

Short Answer

Expert verified

0.19 as a fraction is $\frac{19}{100}$.

Step by step solution

Identify the Decimal Place

Determine the place value of the last digit in the decimal. For example, in the decimal 0.19, the 9 is in the hundredths place.

Write as a Fraction

Write the decimal as a fraction using the place value. Since 0.19 ends in the hundredths place, it becomes $\frac{19}{100}$.

Simplify if Possible

Check if the fraction can be simplified. In this case, $\frac{19}{100}$ is already in its simplest form because 19 and 100 have no common factors other than 1.

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Key Concepts

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

Understanding Place Value

To convert a decimal to a fraction, it's essential to understand place value. Place value helps us determine the value of each digit in a number. For the decimal 0.19, the digit 9 is in the hundredths place.

The first digit after the decimal point is the tenths place.
The second digit after the decimal point is the hundredths place.

Recognizing this helps you write the correct fraction. Every position after the decimal point has a specific place value, and that's crucial to converting decimals accurately.

Simplifying Fractions

After writing a decimal as a fraction, the next step is to simplify it. Simplifying a fraction means reducing it to the smallest possible numerator and denominator. This is done by dividing both the numerator and the denominator by their greatest common divisor (GCD).
In the example of $\frac{19}{100}$, there's no need to simplify further because the GCD of 19 and 100 is 1. However, if you have a fraction like $\frac{20}{100}$, you would simplify it by dividing both the numerator and the denominator by their GCD, which is 20, resulting in $\frac{1}{5}$. Understanding how to simplify fractions makes your answers more concise and easier to understand.

Writing Fractions

Writing fractions correctly is critical to displaying your understanding of numbers. When converting a decimal to a fraction, you use the place value to write the fraction properly. For example, with a decimal like 0.19:

First, identify the place value of the last digit. Here, the final digit 9 is in the hundredths place.
Next, write the fraction based on that place value. So, 0.19 becomes $ \frac{19}{100} $.

Once written correctly, always check to see if the fraction can be simplified. This ensures your final answer is in its simplest form and is easy to understand. Properly writing fractions is an important skill in math.

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91影视

Write each decimal as a fraction. $$ 0.19 $$

Short Answer

Step by step solution

Identify the Decimal Place

Write as a Fraction

Simplify if Possible

Key Concepts

Understanding Place Value

Simplifying Fractions

Writing Fractions

One App. One Place for Learning.

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