Converting Decimals to Fractions

To convert a decimal to a fraction, you are essentially reversing place value.

Step-by-step thinking:

1. Take the digits after the decimal → this becomes the numerator
2. Use the place value → this becomes the denominator
3. Simplify if possible

For example:

• $0.6$ → 6 tenths → $\frac{6}{10}$ → simplify to $\frac{3}{5}$
• $0.75$ → 75 hundredths → $\frac{75}{100}$ → simplify to $\frac{3}{4}$

Compare:

• $0.6 = \frac{6}{10}$ → simplifies nicely
• $0.67 = \frac{67}{100}$ → already simplest (67 is prime)

A common mistake is stopping too early and not simplifying. For instance, leaving $\frac{6}{10}$ instead of reducing it to $\frac{3}{5}$. Another mistake is choosing the wrong denominator.

Mental model: You are “unpacking” the decimal into how many pieces out of a power of 10 it represents.

After converting, you almost always want to simplify the fraction. Why? Because simplified fractions are easier to understand, compare, and use.

To simplify, divide both the numerator and denominator by their greatest common factor (GCF).

For example:

• $\frac{50}{100}$ → divide both by 50 → $\frac{1}{2}$
• $\frac{6}{10}$ → divide both by 2 → $\frac{3}{5}$

Compare:

• $\frac{75}{100}$ → simplifies to $\frac{3}{4}$
• → simplifies to

A common mistake is simplifying only the numerator or denominator, which changes the value. You must divide both by the same number.

Mental model: Simplifying is like reducing a fraction to its “cleanest form” without changing its value.

Decimals greater than 1 combine a whole number with a fractional part. To convert them, you can either split them or convert everything at once.

Method 1 (split):

• $2.3 = 2 + 0.3 = 2 + \frac{3}{10} = 2\frac{3}{10}$

Method 2 (all at once):

• $2.3 = \frac{23}{10}$

Both methods give the same value—one is just written differently.

Compare:

• $3.75 = 3 + 0.75 = 3\frac{3}{4}$
• $3.75 = \frac{375}{100} = \frac{15}{4}$

A common mistake is forgetting to convert the whole number when writing an improper fraction. For example, writing $3.75$ as $\frac{75}{100}$ only accounts for the decimal part.

Mental model: A number like 3.75 is “3 wholes plus a fraction,” or “one big fraction made from all the digits.”

Decimals and fractions appear in different real-world contexts, so being able to switch between them makes your thinking more flexible.

For example:

• Cooking: $0.25$ cups → $\frac{1}{4}$ cup (easier to measure)
• Money: $0.50$ → $\frac{1}{2}$ dollar (helps with mental math)

Compare:

• $0.2$ dollars → $\frac{1}{5}$ of a dollar
• $0.2$ meters → easier to think of as 20 cm (a decimal-based system)

A common mistake is sticking to one format even when it makes the problem harder. The goal is to choose the form that makes the situation clearer.

Mental model: Decimals and fractions are two lenses—switch to the one that makes the picture clearer.