How do I deal with repeating decimals?

Repeating decimals require a trick. For 0.333..., set x = 0.333, then 10x = 3.333. Subtract x from 10x (9x = 3). Solve for x (x = 3/9 = 1/3).

Why convert to fractions?

Fractions are often more precise. 1/3 is exact. 0.33 is an approximation. In engineering and baking, exact ratios often matter more than rounded decimals.

What about whole numbers?

For 3.5, you separate the whole number (3). Then convert .5 to 1/2. Combine them to get 3 1/2 (Mixed Number) or 7/2 (Improper Fraction).

From Point to Part: Decimals to Fractions

Decimals are just fractions with denominators of 10, 100, or 1000. Once you see the pattern, you can't unsee it.

Instant Conversion

Convert any decimal to its simplest fraction form.

Decimal Calculator

Step 1: Write it Over 1

Take your decimal, say 0.75.
Write it as a fraction: 0.75 / 1

Step 2: Remove the Decimal

Count how many digits are after the decimal point. (For 0.75, there are 2 digits). Multiply top and bottom by 1 followed by that many zeros (100).
0.75 x 100 = 75
1 x 100 = 100
New Fraction: 75 / 100

Step 3: Simplify

Find the largest number that divides both.
75 and 100 both divide by 25.
75 / 25 = 3
100 / 25 = 4
Answer: 3/4

Common Conversions to Memorize

0.5 = 1/2
0.25 = 1/4
0.75 = 3/4
0.2 = 1/5
0.125 = 1/8