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Chapter 5: Problem 18

Write each decimal as a fraction or mixed number in simplest form. $$0.4$$

Short Answer

Expert verified
0.4 as a fraction is \( \frac{2}{5} \).

Step by step solution

01

Identify the Decimal Place Value

The decimal 0.4 has the digit 4 in the first decimal place, which represents tenths.
02

Write the Decimal as a Fraction

Since 0.4 represents 4 tenths, we can write it as a fraction: \( \frac{4}{10} \).
03

Simplify the Fraction

To simplify \( \frac{4}{10} \), we identify that both the numerator and the denominator can be divided by their greatest common divisor, which is 2.\( \frac{4 \div 2}{10 \div 2} = \frac{2}{5} \).
04

Conclusion

The simplest form of 0.4 as a fraction is \( \frac{2}{5} \).

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Key Concepts

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

Decimal Place Value
Decimal place value helps us understand where each digit in a decimal number is located and what value they represent. Each position to the right of the decimal point holds a place value that is a power of ten, but it becomes a fraction of ten.
Here's how you can break it down:
  • The first place to the right of the decimal point is the tenths place.
  • The second place is the hundredths place.
  • The third place is the thousandths place, and so on.
Since 0.4 has the digit 4 in the tenths place, it means it represents four-tenths or \( \frac{4}{10} \). This understanding is foundational for converting decimals to fractions, as each digit corresponds to a fractional value depending on its place.
Simplifying Fractions
Once a decimal is expressed as a fraction, it is essential to simplify the fraction to its simplest form. Simplifying a fraction means finding an equivalent fraction where the numerator and the denominator are as small as possible but still represent the same value.

Here鈥檚 how to simplify fractions:
  • First, determine the greatest common divisor (GCD) of both the numerator and the denominator.
  • Divide both the numerator and the denominator by their GCD.
  • This results in a simpler, equivalent fraction.
For example, with the fraction \( \frac{4}{10} \), the GCD of 4 and 10 is 2. Dividing both by 2 gives us \( \frac{2}{5} \), which is the simplest form. Simplified fractions make it easier to work with numbers, especially in calculations.
Numerator and Denominator
In any fraction, the numerator and the denominator are the two key components that tell us what part of a whole we are considering.
  • The **numerator** is the top number of a fraction and indicates how many parts of the whole we have.
  • The **denominator** is the bottom number and shows into how many parts the whole is divided.
For \( \frac{4}{10} \), 4 is the numerator, telling us we have four parts out of ten. The denominator, 10, informs us that these parts make up a whole that is divided into ten equal pieces.
After simplifying, the fraction becomes \( \frac{2}{5} \), with 2 as the numerator and 5 as the denominator, which reflects the same proportion of the whole. Understanding both the numerator and the denominator is crucial not only for simplifying fractions but also for performing operations such as addition or subtraction of fractions.

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Most popular questions from this chapter

Find sum or difference. Write in simplest form. \(7 \frac{4}{7}-2 \frac{5}{7}\)

Write each decimal as a fraction or mixed number in simplest form. $$3.625$$

Find each quotient. Use an area model if necessary. $$-\frac{1}{2} \div \frac{5}{6}$$

The table shows the weight of Leon's dog during its first five years. $$\begin{array}{|c|c|}\hline \text { Age } & \text { Weigh } \\\\\hline(\text {years}) & (\text { pounds }) \\\\\hline 1 & 17 \frac{2}{8} \\\\\hline 2 & 18 \frac{5}{8} \\\\\hline 3 & 19 \frac{4}{8} \\\\\hline 4 & 18 \frac{3}{8} \\\\\hline 5 & 20 \frac{7}{8} \\\\\hline\end{array}$$ How much weight did Leon's dog lose between ages 3 and 4?

Find the least common multiple (LCM) of each pair of numbers or monomials. $$\frac{4}{5}, \frac{1}{2}$$
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