Decimal to Fraction Notes
This Decimal to Fraction Calculator helps you turn a decimal into a fraction and shows the working clearly at every step. Start by writing the decimal over 1, then multiply the numerator and the denominator by 10 for each digit after the decimal point, which slides the point away and leaves a whole number as the numerator. Then check whether the answer can be written with smaller numbers. Following the same pattern every time is what makes converting decimals easy to picture, check, and repeat on your own with any decimal.
Step-by-step method
- Set up the problem.
- Multiply the numerator and the denominator by 10 for each digit after the decimal point, so the numerator becomes a whole number.
- Simplify the answer at the end if you can. This step is Simplifying of Fractions.
See Example 1 Hide Example 1
Problem
Approach
Step-by-step method
- Set up the problem.
- Multiply the numerator and the denominator by 10 for each digit after the decimal point, so the numerator becomes a whole number.
- Simplify the answer at the end if you can. This step is Simplifying of Fractions.
Step 1
Step 1 - Set up the problem.
In this problem: Write \(0.75\) as a fraction over \(1\).
Step 2
Step 2 - Multiply the numerator and the denominator by 10 for each digit after the decimal point, so the numerator becomes a whole number.
In this problem: There are \(2\) digits after the decimal point, so we multiply by \(\frac{100}{100}\).
Step 3
Step 3 - Simplify the answer at the end if you can. This step is Simplifying of Fractions.
In this problem: The biggest number that divides both \(75\) and \(100\) is \(25\). Dividing each by it gives \(75\div 25 = 3\) and \(100\div 25 = 4\).
Problem
Approach
Step-by-step method
- Set up the problem.
- List the numbers that divide the numerator, and the numbers that divide the denominator. The biggest one on both lists is the one to use.
- Divide the numerator and the denominator by that number.
Step 1
Step 1 - Set up the problem.
In this problem: We are simplifying \(\frac{75}{100}\).
Step 2
Step 2 - List the numbers that divide the numerator, and the numbers that divide the denominator. The biggest one on both lists is the one to use.
In this problem: Listing what divides each one, both lists contain \(1, 5, 25\). The biggest of those is \(25\), so \(25\) is the number to divide by.
Step 3
Step 3 - Divide the numerator and the denominator by that number.
In this problem: Divide both by \(25\): \(75 \div 25 = 3\) and \(100 \div 25 = 4\).
Final Answer
Final Answer
See Example 2 Hide Example 2
Problem
Approach
Step-by-step method
- Set up the problem.
- Multiply the numerator and the denominator by 10 for each digit after the decimal point, so the numerator becomes a whole number.
- Simplify the answer at the end if you can. This step is Simplifying of Fractions.
Step 1
Step 1 - Set up the problem.
In this problem: Write \(2.5\) as a fraction over \(1\).
Step 2
Step 2 - Multiply the numerator and the denominator by 10 for each digit after the decimal point, so the numerator becomes a whole number.
In this problem: There is \(1\) digit after the decimal point, so we multiply by \(\frac{10}{10}\).
Step 3
Step 3 - Simplify the answer at the end if you can. This step is Simplifying of Fractions.
In this problem: The biggest number that divides both \(25\) and \(10\) is \(5\). Dividing each by it gives \(25\div 5 = 5\) and \(10\div 5 = 2\).
Problem
Approach
Step-by-step method
- Set up the problem.
- List the numbers that divide the numerator, and the numbers that divide the denominator. The biggest one on both lists is the one to use.
- Divide the numerator and the denominator by that number.
Step 1
Step 1 - Set up the problem.
In this problem: We are simplifying \(\frac{25}{10}\).
Step 2
Step 2 - List the numbers that divide the numerator, and the numbers that divide the denominator. The biggest one on both lists is the one to use.
In this problem: Listing what divides each one, both lists contain \(1, 5\). The biggest of those is \(5\), so \(5\) is the number to divide by.
Step 3
Step 3 - Divide the numerator and the denominator by that number.
In this problem: Divide both by \(5\): \(25 \div 5 = 5\) and \(10 \div 5 = 2\).
Final Answer
Final Answer
See Example 3 Hide Example 3
Problem
Approach
Step-by-step method
- Set up the problem.
- Multiply the numerator and the denominator by 10 for each digit after the decimal point, so the numerator becomes a whole number.
- Simplify the answer at the end if you can. This step is Simplifying of Fractions.
Step 1
Step 1 - Set up the problem.
In this problem: Write \(0.35\) as a fraction over \(1\).
Step 2
Step 2 - Multiply the numerator and the denominator by 10 for each digit after the decimal point, so the numerator becomes a whole number.
In this problem: There are \(2\) digits after the decimal point, so we multiply by \(\frac{100}{100}\).
Step 3
Step 3 - Simplify the answer at the end if you can. This step is Simplifying of Fractions.
In this problem: The biggest number that divides both \(35\) and \(100\) is \(5\). Dividing each by it gives \(35\div 5 = 7\) and \(100\div 5 = 20\).
Problem
Approach
Step-by-step method
- Set up the problem.
- List the numbers that divide the numerator, and the numbers that divide the denominator. The biggest one on both lists is the one to use.
- Divide the numerator and the denominator by that number.
Step 1
Step 1 - Set up the problem.
In this problem: We are simplifying \(\frac{35}{100}\).
Step 2
Step 2 - List the numbers that divide the numerator, and the numbers that divide the denominator. The biggest one on both lists is the one to use.
In this problem: Listing what divides each one, both lists contain \(1, 5\). The biggest of those is \(5\), so \(5\) is the number to divide by.
Step 3
Step 3 - Divide the numerator and the denominator by that number.
In this problem: Divide both by \(5\): \(35 \div 5 = 7\) and \(100 \div 5 = 20\).
Final Answer
Final Answer
See Example 4 Hide Example 4
Problem
Approach
Step-by-step method
- Set up the problem.
- Multiply the numerator and the denominator by 10 for each digit after the decimal point, so the numerator becomes a whole number.
- Simplify the answer at the end if you can. This step is Simplifying of Fractions.
Step 1
Step 1 - Set up the problem.
In this problem: Write \(3.2\) as a fraction over \(1\).
Step 2
Step 2 - Multiply the numerator and the denominator by 10 for each digit after the decimal point, so the numerator becomes a whole number.
In this problem: There is \(1\) digit after the decimal point, so we multiply by \(\frac{10}{10}\).
Step 3
Step 3 - Simplify the answer at the end if you can. This step is Simplifying of Fractions.
In this problem: The biggest number that divides both \(32\) and \(10\) is \(2\). Dividing each by it gives \(32\div 2 = 16\) and \(10\div 2 = 5\).
Problem
Approach
Step-by-step method
- Set up the problem.
- List the numbers that divide the numerator, and the numbers that divide the denominator. The biggest one on both lists is the one to use.
- Divide the numerator and the denominator by that number.
Step 1
Step 1 - Set up the problem.
In this problem: We are simplifying \(\frac{32}{10}\).
Step 2
Step 2 - List the numbers that divide the numerator, and the numbers that divide the denominator. The biggest one on both lists is the one to use.
In this problem: Listing what divides each one, both lists contain \(1, 2\). The biggest of those is \(2\), so \(2\) is the number to divide by.
Step 3
Step 3 - Divide the numerator and the denominator by that number.
In this problem: Divide both by \(2\): \(32 \div 2 = 16\) and \(10 \div 2 = 5\).
Final Answer
Final Answer