Definition
Fraction-decimal conversion
Fraction-decimal conversion rewrites the same value in fraction notation or decimal notation.
What it means
The notation changes, but the number does not. Tenths and hundredths convert directly: 7/10 is 0.7. For other fractions, divide the numerator by the denominator. To turn a terminating decimal back into a fraction, use its last place to choose the denominator, then simplify.
Remember it
Same point on the number line, different notation.
Example
3/8 = 0.375 because 3 ÷ 8 = 0.375. Going back, 0.375 means 375 thousandths, so 0.375 = 375/1000. Dividing numerator and denominator by 125 simplifies this to 3/8.
Watch for
Some decimals repeat forever. For example, 1/3 = 0.333… exactly; 0.3 is only an approximation to 1/3.
Common mix-up
Do not copy the numerator and denominator as decimal digits: 3/8 is 0.375, not 0.38.
Exact meaning
Fraction-decimal conversion rewrites the same rational number in fraction notation or decimal notation without changing its value. Dividing the numerator by the denominator gives a terminating or repeating decimal; a terminating decimal can be written over 10, 100, 1000, and so on, then simplified.