Decimal to Fraction
- What Do You Mean by Decimal to Fraction?
- How to Convert Decimal to Fraction
- Converting Repeating Decimal to Fraction
- Converting Decimals to Mixed Number Fractions
- Converting Negative Decimal to Fraction
- Converting Decimal to Fraction: Inches
- Solved Examples
- Practice Problems
- Frequently Asked Questions
What Do You Mean by Decimal to Fraction?
A decimal is a way of representing a number that is not a whole number, while a fraction represents a part of a whole. Converting a decimal to a fraction involves expressing the decimal number as a ratio of two integers. To do this, we identify the place value of each digit in the decimal number. The place value of each digit determines its contribution to the overall value of the number.
How to Convert Decimal to Fraction?
`1`. Identify the Decimal Place Value: Begin by identifying the place value of each digit in the decimal number. The digits to the left of the decimal point represent whole numbers, while those to the right represent fractions of a whole.
`2`. Write the Decimal as a Fraction: Write the digits of the decimal number as the numerator of the fraction. The denominator of the fraction will be based on the place value of the rightmost digit after the decimal point.
`3`. Simplify the Fraction (if necessary): After writing the decimal as a fraction, simplify it by dividing both the numerator and the denominator by their greatest common factor (GCF) to express the fraction in its simplest form.
Example `1`: Convert the decimal `0.375` to its equivalent fraction.
Solution:
`1`. Identify Decimal Place Values: In the decimal `0.375`, the digit `3` is in the tenth place, `7` is in the hundredth place, and `5` is in the thousandth place.
`2`. Write Decimal as Fraction: Write the digits of the decimal as the numerator of the fraction. The denominator will be based on the place value of the rightmost digit after the decimal point, that is the thousandth place. So, we have \( \frac{375}{1000} \).
`3`. Simplify Fraction (if necessary): To simplify the fraction, we find the greatest common factor (GCF) of the numerator and the denominator, which is `125`. Dividing both numerator and denominator by `125`, we get \( \frac{3}{8} \).
Therefore, the fraction equivalent of the decimal `0.375` is \( \frac{3}{8} \).
Example `2`: Convert the decimal `0.75` to its equivalent fraction.
Solution:
`1`. Identify Decimal Place Values: In the decimal `0.75`, the digit `7` is in the tenth place and `5` is in the hundredth place.
`2`. Write Decimal as Fraction: Write the digits of the decimal as the numerator of the fraction. The denominator will be based on the place value of the rightmost digit after the decimal point, that is the hundredth place. So, we have \( \frac{75}{100} \).
`3`. Simplify Fraction (if necessary): To simplify the fraction, we find the greatest common factor (GCF) of the numerator and the denominator, which is `25`. Dividing both numerator and denominator by `25`, we get \( \frac{3}{4} \).
Therefore, the fraction equivalent of the decimal `0.75` is \( \frac{3}{4} \).
Converting Repeating Decimal to Fraction
`1`. Identify the repeating pattern: First, identify the repeating pattern in the decimal. This pattern is the set of digits that repeat indefinitely after the decimal point.
`2`. Assign variable: Assign a variable to represent the repeating pattern. This variable will help in formulating an equation to find the fraction equivalent to the repeating decimal.
`3`. Write an equation: Formulate an equation by subtracting the original number from a multiple of the repeating decimal that removes the repeating part. This process eliminates the repeating digits, leaving only the non-repeating digits.
`4`. Solve for the variable: Solve the equation obtained in the previous step to find the variable's value representing the repeating pattern.
`5`. Simplify the fraction (if necessary): If the fraction obtained in the previous step is not in its simplest form, simplify it by finding the greatest common factor (GCF) of the numerator and denominator and dividing both by it.
`6`. Write the simplified fraction: Express the simplified fraction as the final result, representing the repeating decimal in fractional form.
Example: Convert the repeating decimal `0.454545...` to its equivalent fraction.
Solution:
`1`. Identify the repeating pattern: In the decimal `0.454545...`, the digits `45` repeat infinitely.
`2`. Assign variable: Let `x` represent the repeating decimal. So, we have `x = 0.454545…`
`3`. Write an equation: Subtracting `x` from `100x` eliminates the repeating part:
`100x - x = 45.4545... - 0.4545... `
`99x= 45`
`4`. Solve for the variable: Solving the equation `99x = 45` gives `x = 45/99`.
`5`. Simplify the fraction (if necessary): The fraction `45/99` can be simplified by finding the greatest common factor (GCF) of the numerator and denominator, which is `9`. Dividing both the numerator and denominator by `9`, we get the simplified fraction `5/11`.
`6`. Write the simplified fraction: Therefore, the fraction equivalent of the repeating decimal `0.454545...` is `5/11`.
Thus, the repeating decimal `0.454545...` can be represented as the fraction `5/11`.
Converting Decimals to Mixed Number Fractions
`1`. Identify the whole number part: Determine the whole number part of the decimal, which appears to the left of the decimal point. This whole number will become the whole number part of the mixed number fraction.
`2`. Identify the fractional part: Examine the digits after the decimal point. These digits represent the fractional part of the mixed number fraction.
`3`. Convert fractional part to fraction: Write down the digits after the decimal point as the numerator of the fraction. The denominator will depend on the place value of the rightmost digit after the decimal point. For example, if the decimal is `0.75`, the fraction would be \( \frac{75}{100} \).
`4`. Simplify the fraction (if necessary): Simplify the fraction obtained in the previous step by finding the greatest common factor (GCF) of the numerator and denominator. Then, divide both the numerator and denominator by their GCF to express the fraction in its simplest form.
`5`. Combine whole number and fraction: Combine the whole number obtained in Step `1` with the simplified fraction obtained in Step `4` to form the mixed number fraction.
Example: Convert the decimal `6.75` to its equivalent mixed number fraction.
Solution:
`1`. Identify the whole number part: The whole number part of the decimal `6.75` is `6`.
`2`. Identify the fractional part: The fractional part of the decimal `6.75` is `0.75`.
`3`. Convert fractional part to fraction: Write down the digits after the decimal point `(75)` as the numerator of the fraction. Since there are two digits after the decimal point, the denominator will be `100`. So, the fraction is \( \frac{75}{100} \).
`4`. Simplify the fraction: Simplify \( \frac{75}{100} \) by finding the greatest common factor (GCF) of the numerator and denominator. The GCF of `75` and `100` is `25`. Dividing both numerator and denominator by `25`, we get \( \frac{75 \div 25}{100 \div 25} = \frac{3}{4} \).
`5`. Combine whole number and fraction: Combine the whole number part `(6)` with the simplified fraction ( \( \frac{3}{4} \)) to form the mixed number fraction.
Therefore, the mixed number fraction equivalent of the decimal `6.75` is \( 6 \frac{3}{4} \).
Thus, the decimal `6.75` can be represented as the mixed number fraction \( 6 \frac{3}{4} \).
Converting Negative Decimal to Fraction
Converting a negative decimal to a fraction follows similar steps as converting a positive decimal, with special attention paid to preserving the negative sign. Here's a systematic approach:
`1`. Identify the decimal part: Determine the decimal part of the negative decimal number. This part lies to the right of the decimal point.
`2`. Write the decimal as a fraction: Write down the digits after the decimal point as the numerator of the fraction. The denominator will depend on the place value of the rightmost digit after the decimal point.
`3`. Account for the negative sign: Ensure that the negative sign is preserved in the fraction. This can be achieved by placing the negative sign in front of the whole number part.
`4`. Simplify the fraction (if necessary): Simplify the fraction obtained in the previous step by finding the greatest common factor (GCF) of the numerator and denominator. Divide both the numerator and denominator by their GCF to express the fraction in its simplest form.
Example: Convert the negative decimal `-1.625` to its equivalent fraction.
Solution:
`1`. Identify the decimal part: The decimal part of `-0.625` is `.625`.
`2`. Write the decimal as a fraction: Write down the digits after the decimal point as the numerator of the fraction. Since there are three digits after the decimal point, the denominator will be `1000`. So, the fraction is \( \frac{625}{1000} \).
`3`. Account for the negative sign: Preserve the negative sign in the fraction. The negative sign should be placed in front of the whole number part.
`4`. Simplify the Fraction: Simplify \( \frac{625}{1000} \) by finding the greatest common divisor (GCD) of the numerator and denominator. The GCD of `625` and `1000` is `125`. Dividing both numerator and denominator by `125`, we get \( \frac{625 \div 125}{1000 \div 125} = \frac{5}{8} \).
`5`. Combine negative sign and fraction: Combine the negative sign with the fraction obtained in the previous step.
Therefore, the fraction equivalent of the negative decimal `-0.625` is \( -\frac{5}{8} \).
Converting Decimal to Fraction: Inches
Converting a decimal to a fraction when dealing with measurements like inches requires attention to detail. Here's a systematic approach:
`1`. Identify the decimal part: Determine the decimal part of the measurement, representing the fraction of an inch.
`2`. Write the decimal as a fraction: Express the decimal part as a fraction. The denominator will typically be a power of `10` corresponding to the number of decimal places. For example, `0.25` inches would be \( \frac{25}{100} \).
`3`. Simplify the fraction (if necessary): Simplify the fraction to its lowest terms, if possible, by finding the greatest common factor (GCF) of the numerator and denominator and dividing both by it.
`4`. Combine with whole number (if applicable): If there's a whole number part in the measurement, include it alongside the fraction. For instance, `2.5` inches would be written as \( 2 \frac{1}{2} \).
Example: Convert the decimal `0.875` inches to a fraction.
Solution:
`1`. Identify the decimal part: In `0.875` inches, the decimal part is `0.875`.
`2`. Write the decimal as a fraction: Expressing `0.875` as a fraction, we get \( \frac{875}{1000} \).
`3`. Simplify the fraction: Simplifying \( \frac{875}{1000} \) by finding the greatest common factor (GCF) of `875` and `1000`, which is `125`. Dividing both numerator and denominator by `125`, we get \( \frac{875 \div 125}{1000 \div 125} = \frac{7}{8} \).
Therefore, the fraction equivalent of `0.875` inches is \( \frac{7}{8} \).
Hence, `0.875` inches is equivalent to \( \frac{7}{8} \) of an inch.
Solved Examples
Example `1`. Turn decimal `0.6` into a fraction in its simplest form.
Solution:
For the decimal `0.6`:
`1`. Write `6` as the numerator.
`2`. Since `6` is in the tenth place, the denominator is `10`.
`3`. Simplify the fraction if necessary.
Therefore, `0.6` as a fraction is \( \frac{6}{10} \).
To simplify the fraction, find the greatest common factor (GCF) of the numerator and denominator, which is `2`. Divide both the numerator and denominator by `2`:
`\frac{6 \div 2}{10 \div 2} = \frac{3}{5}`
So, `0.6` as a fraction in its simplest form is \( \frac{3}{5} \).
Example `2`: Convert the repeating decimal `0.121212...` to its equivalent fraction.
Solution:
`1`. In the decimal `0.121212...`, the digits `12` repeat infinitely.
`2`. Let `x` represent the repeating decimal. So, we have `x = 0.121212...`
`3`. Subtracting `x` from `100x` eliminates the repeating part:
`100x - x = 12.1212... - 0.1212... `
`99x = 12`
`4`. Solving the equation `99x = 12` gives `x = 12/99`.
`5`. Simplifying the expression `12/99` gives us `4/33`.
Therefore, the fraction equivalent to the repeating decimal `0.121212...` is `4/33`.
Practice Problems
Q`1`. Convert the decimal `0.625` inches to its equivalent fraction.
- \( \frac{3}{5} \)
- \( \frac{5}{8} \)
- \( \frac{2}{5} \)
- \( \frac{5}{6} \)
Answer: b
Q`2`. Convert the decimal `1.375` inches to its equivalent mixed number fraction.
- \( 1 \frac{3}{8} \)
- \( 1 \frac{5}{8} \)
- \( 1 \frac{7}{8} \)
- \( 1 \frac{1}{2} \)
Answer: a
Q`3`. Convert the repeating decimal `0.343434….` inches to its equivalent fraction.
- \( \frac{19}{53} \)
- \( \frac{34}{99} \)
- \( \frac{37}{95} \)
- \( \frac{12}{33} \)
Answer: b
Q`4`. Convert the decimal `0.875` inches to a fraction.
- \( \frac{7}{8} \)
- \( 1 \frac{3}{4} \)
- \( 1 \frac{1}{8} \)
- \( \frac{3}{4} \)
Answer: a
Q`5`. Convert the decimal `3.25` inches to a mixed number fraction.
- \( 3 \frac{1}{4} \)
- \( 3 \frac{2}{3} \)
- \( 3 \frac{3}{4} \)
- \( 3 \frac{1}{8} \)
Answer: a
Frequently Asked Questions
Q`1`. How do you convert a decimal to a fraction when measuring in inches?
Answer: To convert a decimal to a fraction when measuring in inches, write down the decimal as a fraction, then simplify it if necessary. For example, `0.75` inches is equivalent to \( \frac{75}{100} \), which simplifies to \( \frac{3}{4} \).
Q`2`. Can a negative decimal be converted to a fraction for measurements like temperatures?
Answer: Yes, negative decimals can be converted to fractions. Follow the same steps as with positive decimals, ensuring to preserve the negative sign where appropriate. For example, `-1.5°F` can be represented as \( -1 \frac{1}{2}°F \).
Q`3`. What if the decimal part of a measurement in inches is repeating?
Answer: If the decimal part is repeating, follow the steps to convert a repeating decimal to a fraction. Identify the repeating pattern and express it as a fraction. For instance, `0.333...` inches is \( \frac{1}{3} \).
Q`4`. Is it necessary to simplify the fraction when converting a decimal to a fraction for measurements like inches?
Answer: Simplifying the fraction is not always necessary, but it is preferred as it provides a clearer representation. However, leaving the fraction not simplified is also acceptable in some contexts.
Q`5`. What are some of the advantages of converting a decimal to its equivalent fraction?
Answer: Converting a decimal to its equivalent fraction can be useful for several reasons:
Ease of Understanding: Fractions are often easier to visualize and understand than decimals, especially while solving mathematic problems or dealing with practical applications.
Fractions can be compared more easily than decimals, especially when dealing with fractions that have common denominators.
Fractions can represent certain values more simply than decimals, particularly recurring or repeating decimals which can be cumbersome to write out.
In some situations, fractions may be preferred or required over decimals, such as when working with certain measurements or in specific mathematical operations.