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Chapter 0: Problem 5

Write each decimal as a fraction. (Do not write in lowest terms.) 0.4

Short Answer

Expert verified
0.4 = \( \frac{4}{10} \)

Step by step solution

01

- Write the Decimal as a Fraction

To convert the decimal 0.4 to a fraction, first recognize that the number is in the tenths place. This means we can write it as: 0.4 = \( \frac{4}{10} \)
02

- Confirm Fraction Form

Verify that the decimal has been correctly written as a fraction. For 0.4, this results in: 0.4 = \( \frac{4}{10} \)

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Key Concepts

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

tenths place
Understanding the tenths place is crucial when converting decimals to fractions. In a decimal number, the tenths place is the first position immediately to the right of the decimal point. For example, in the decimal 0.4, the digit 4 is in the tenths place.

This position indicates the value of the digit as a fraction of ten. That is, it tells us that we are working with parts of ten. In this case, 0.4 means 4 parts out of 10. Therefore, to convert 0.4 into a fraction, we use the value of the tenths place, resulting in: \ \ 0.4 = \( \frac{4}{10} \)

Keep in mind:
  • The tenths place is the key to understanding how to convert any decimal with one digit after the decimal point into a fraction.
  • Simply recognize the digit in the tenths place, and that number will be the numerator of a fraction with a denominator of 10.
decimal to fraction conversion
Converting decimals to fractions is a straightforward process once you understand the place value of the decimal. For example, converting 0.4 to a fraction involves a few easy steps:

  • Identify the decimal and determine its place value. In 0.4, the digit 4 is in the tenths place.
  • Express the decimal as a fraction using the place value. For 0.4, this means writing it as \( \frac{4}{10} \).


This process is equally applicable to decimals with more digits:
  • For 0.25, the digit 5 is in the hundredths place, so it would be written as \( \frac{25}{100} \).
  • For 0.375, the digit 5 is in the thousandths place, making it \( \frac{375}{1000} \).
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    Remember, the key steps are always identifying the place value and then converting it into a fraction accordingly. This method not only works for simpler decimals like 0.4, but for any decimal number.
fraction representation
Fraction representation is a method of expressing numbers that are not whole as a ratio of two integers. In the case of converting decimals to fractions, we frequently deal with tenths, hundredths, and thousandths denominators.

For example, the decimal 0.4 is represented as the fraction \( \frac{4}{10} \), signifying 4 parts out of 10. This conversion helps in:

  • Visualizing the part-to-whole relationship, which is particularly important in various mathematical calculations.
  • Making arithmetic operations like addition, subtraction, multiplication, and division easier when dealing with fractions rather than decimals.
  • Comparing values: Fractions can be more intuitive for comparing and understanding proportions.


When you write a decimal as a fraction, it gives a clearer picture of the value's magnitude concerning the whole. While the original decimal might seem abstract, the fraction format simplifies understanding by providing a tangible reference.

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Most popular questions from this chapter

Estimate the best approximation for the sum. $$ \frac{14}{26}+\frac{98}{99}+\frac{100}{51}+\frac{90}{31}+\frac{13}{27} $$ A. 5 B. 6 C. 7 D. 8

Find each sum or difference, and write it in lowest terms as needed. $$ 6 \frac{1}{4}-5 \frac{1}{3} $$

What is \(25 \%\) of \(120 ?\)

Find each sum or difference, and write it in lowest terms as needed. $$ 3 \frac{4}{5}-1 \frac{4}{9} $$

Write each improper fraction as a mixed number. $$ \frac{67}{13} $$
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