AI Tutor
If you have 33 quarters, you hold 34\frac{3}{4} of a dollar in your hand — but a cash register screen displays it as $0.75.
How do fractions like 34\frac{3}{4} translate so neatly into decimals like 0.750.75 without any long division?

The Base-Ten Secret

Our decimal number system is built on place value, where each spot to the right of the decimal point represents a fraction with a denominator of 1010, 100100, or 10001000.
Because decimals naturally speak in tenths, hundredths, and thousandths, any fraction whose bottom number is 1010, 100100, or 10001000 turns into a decimal instantly.
For example, 710\frac{7}{10} is written as 0.70.7, and 39100\frac{39}{100} is written as 0.390.39.
What if your fraction has a denominator like 55 or 2020 instead of 1010 or 100100?

Creating Friendly Denominators

We can build equivalent fractions — fractions that represent the exact same value — by multiplying the numerator (top number) and the denominator (bottom number) by the same multiplier.
To convert 35\frac{3}{5} into a decimal, find what factor turns the denominator 55 into 1010.
Since 5×2=105 \times 2 = 10, we multiply both the top and bottom by 22 to get 610\frac{6}{10}, which gives us 0.60.6.