Converting Fractions to Decimals Practice

A fraction represents division: its numerator is divided by its denominator. For 3/4, calculate 3 ÷ 4. The numerator tells you how many units are being shared, and the denominator tells you the number of equal groups. Since three units shared among four groups gives less than one unit per group, you can predict that the decimal answer will be below one.

Sometimes an equivalent fraction gives the decimal immediately. Multiply both parts by the same number to make the denominator 10, 100, or 1000. For 3/4, multiplying by 25 gives 75/100. Seventy five hundredths is 0.75. This method works neatly when the denominator divides a suitable power of ten, and it gives a useful check on a division calculation.

For denominators such as 8, thousandths can be convenient. Because 8 × 125 = 1000, the fraction 7/8 equals 875/1000, or 0.875. Keep placeholder zeros when the numerator has fewer digits than the denominator’s place count. For example, 7/1000 is 0.007. Writing 0.7 would describe seven tenths, a much larger quantity.

An improper fraction can produce a value greater than one. Divide as usual, keeping the whole number part of the quotient. A mixed number already separates that whole part: 2 + 3/4 becomes 2 + 0.75 = 2.75. Convert its fractional part first, then add the whole part back. Do not multiply the whole part by the decimal you found.

A fraction in simplest form terminates in decimal notation when its denominator contains only factors of 2 and 5. Other denominators can produce repeating decimals, such as 1/3 = 0.333… . A rounded decimal is then an approximation rather than an exact equivalent. This practice uses terminating fractions. To check any answer here, multiply the decimal by the original denominator and confirm that it recovers the numerator.