So, 0.125 as a simplified fraction is \( \frac{1}{8} \).
5
Solved Example
Medium Level
Sarah ate 0.6 of a pizza. Her brother ate 0.3 of the same pizza. What fraction of the pizza did Sarah eat? What fraction did her brother eat? Can you write these as fractions with the same denominator?
Solution & Explanation
Let's break this down:
Sarah's portion:
Decimal: 0.6
Fraction: \( \frac{6}{10} \)
Simplified fraction: \( \frac{3}{5} \)
Brother's portion:
Decimal: 0.3
Fraction: \( \frac{3}{10} \)
Simplified fraction: \( \frac{3}{10} \) (already in simplest form)
Fractions with the same denominator:
Sarah ate \( \frac{6}{10} \) of the pizza.
Her brother ate \( \frac{3}{10} \) of the pizza.
Both fractions have the same denominator (10), so they are ready to be compared or added if needed.
💡 Key Concept: When converting decimals to fractions, the denominator is determined by the place value of the last digit. For decimals like 0.6 and 0.3, the tenths place is the highest, leading to a denominator of 10.
6
Solved Example
Medium Level
A recipe calls for 0.4 cups of sugar. Write this amount as a fraction. If the recipe is doubled, how many cups of sugar would be needed in total? Write the total as a mixed number or improper fraction.
Solution & Explanation
Let's solve this:
Amount of sugar as a fraction:
Decimal: 0.4
Fraction: \( \frac{4}{10} \)
Simplified fraction: \( \frac{2}{5} \) cups of sugar.
Doubling the recipe:
If the recipe is doubled, Sarah needs \( 0.4 + 0.4 = 0.8 \) cups of sugar.
As an improper fraction, this is \( \frac{4}{5} \).
📌 Note: Since 0.8 is less than 1, it's often written as a simple fraction rather than a mixed number. \( \frac{8}{10} \) simplifies to \( \frac{4}{5} \).
7
Solved Example
Real World Example
Maria is running a race. She has completed 0.75 of the race. What fraction of the race has Maria completed?
Solution & Explanation
Let's find out what fraction of the race Maria has completed:
Step 1: The decimal is 0.75.
Step 2: The digits after the decimal are 75. This is the numerator.
Step 3: There are two digits after the decimal, so the denominator is 100.
Step 4: The fraction is \( \frac{75}{100} \).
Step 5: Simplify the fraction. Both 75 and 100 are divisible by 25.
Maria has completed \( \frac{3}{4} \) of the race.
💡 Real-world connection: This is like saying Maria has completed three-quarters of the race.
8
Solved Example
Real World Example
A baker uses 0.5 pounds of flour for a cake. Write this amount as a fraction. If the baker needs to make 3 cakes, how many pounds of flour would be needed in total? Write the total as a mixed number.
Solution & Explanation
Let's calculate the flour needed:
Amount of flour for one cake as a fraction:
Decimal: 0.5
Fraction: \( \frac{5}{10} \)
Simplified fraction: \( \frac{1}{2} \) pound of flour.
Total flour for 3 cakes:
If 1 cake needs \( \frac{1}{2} \) pound, then 3 cakes need \( 3 \times \frac{1}{2} \) pounds.
\( 3 \times \frac{1}{2} = \frac{3}{2} \) pounds.
To write this as a mixed number, divide 3 by 2. 3 \div ided by 2 is 1 with a remainder of 1.
So, \( \frac{3}{2} \) pounds is equal to \( 1 \frac{1}{2} \) pounds.
The baker would need \( 1 \frac{1}{2} \) pounds of flour in total.
👉 Think about it: This means the baker needs one whole pound and half of another pound of flour.
4th Grade Math: Decimals to Fractions Practice Questions
Example 1:
Convert the decimal 0.7 into a fraction.
Solution:
Here's how to convert 0.7 to a fraction:
Step 1: Identify the place value of the last digit in the decimal. In 0.7, the digit 7 is in the tenths place.
Step 2: Write the decimal as a fraction with the digit(s) after the decimal point as the numerator. So, we have 7.
Step 3: The denominator of the fraction will be a power of 10 corresponding to the place value. Since it's the tenths place, the denominator is 10.
Step 4: Combine the numerator and denominator to form the fraction.
Therefore, 0.7 is equal to \( \frac{7}{10} \).
💡 Tip: The number of digits after the decimal point tells you how many zeros will be in the denominator (after the 1).
Example 2:
Express the decimal 0.25 as a fraction in its simplest form.
Solution:
Let's convert 0.25 to a fraction:
Step 1: The digits after the decimal are 25. This will be our numerator.
Step 2: There are two digits after the decimal point (2 and 5), so the denominator will be 100 (for hundredths).
Step 3: So, 0.25 is equal to \( \frac{25}{100} \).
Step 4: Now, simplify the fraction. Both 25 and 100 can be divided by 25.
So, 0.125 as a simplified fraction is \( \frac{1}{8} \).
Example 5:
Sarah ate 0.6 of a pizza. Her brother ate 0.3 of the same pizza. What fraction of the pizza did Sarah eat? What fraction did her brother eat? Can you write these as fractions with the same denominator?
Solution:
Let's break this down:
Sarah's portion:
Decimal: 0.6
Fraction: \( \frac{6}{10} \)
Simplified fraction: \( \frac{3}{5} \)
Brother's portion:
Decimal: 0.3
Fraction: \( \frac{3}{10} \)
Simplified fraction: \( \frac{3}{10} \) (already in simplest form)
Fractions with the same denominator:
Sarah ate \( \frac{6}{10} \) of the pizza.
Her brother ate \( \frac{3}{10} \) of the pizza.
Both fractions have the same denominator (10), so they are ready to be compared or added if needed.
💡 Key Concept: When converting decimals to fractions, the denominator is determined by the place value of the last digit. For decimals like 0.6 and 0.3, the tenths place is the highest, leading to a denominator of 10.
Example 6:
A recipe calls for 0.4 cups of sugar. Write this amount as a fraction. If the recipe is doubled, how many cups of sugar would be needed in total? Write the total as a mixed number or improper fraction.
Solution:
Let's solve this:
Amount of sugar as a fraction:
Decimal: 0.4
Fraction: \( \frac{4}{10} \)
Simplified fraction: \( \frac{2}{5} \) cups of sugar.
Doubling the recipe:
If the recipe is doubled, Sarah needs \( 0.4 + 0.4 = 0.8 \) cups of sugar.
As an improper fraction, this is \( \frac{4}{5} \).
📌 Note: Since 0.8 is less than 1, it's often written as a simple fraction rather than a mixed number. \( \frac{8}{10} \) simplifies to \( \frac{4}{5} \).
Example 7:
Maria is running a race. She has completed 0.75 of the race. What fraction of the race has Maria completed?
Solution:
Let's find out what fraction of the race Maria has completed:
Step 1: The decimal is 0.75.
Step 2: The digits after the decimal are 75. This is the numerator.
Step 3: There are two digits after the decimal, so the denominator is 100.
Step 4: The fraction is \( \frac{75}{100} \).
Step 5: Simplify the fraction. Both 75 and 100 are divisible by 25.
Maria has completed \( \frac{3}{4} \) of the race.
💡 Real-world connection: This is like saying Maria has completed three-quarters of the race.
Example 8:
A baker uses 0.5 pounds of flour for a cake. Write this amount as a fraction. If the baker needs to make 3 cakes, how many pounds of flour would be needed in total? Write the total as a mixed number.
Solution:
Let's calculate the flour needed:
Amount of flour for one cake as a fraction:
Decimal: 0.5
Fraction: \( \frac{5}{10} \)
Simplified fraction: \( \frac{1}{2} \) pound of flour.
Total flour for 3 cakes:
If 1 cake needs \( \frac{1}{2} \) pound, then 3 cakes need \( 3 \times \frac{1}{2} \) pounds.
\( 3 \times \frac{1}{2} = \frac{3}{2} \) pounds.
To write this as a mixed number, divide 3 by 2. 3 \div ided by 2 is 1 with a remainder of 1.
So, \( \frac{3}{2} \) pounds is equal to \( 1 \frac{1}{2} \) pounds.
The baker would need \( 1 \frac{1}{2} \) pounds of flour in total.
👉 Think about it: This means the baker needs one whole pound and half of another pound of flour.