Kid-friendly explanation
A terminating decimal is a decimal that stops. The digits after the decimal point do not go on forever. For example, 2.4 stops after the 4, and 0.375 stops after the 5. A decimal like 0.3333... that keeps going and never stops is not a terminating decimal!
Worked examples
Example 1 (middle school): Convert a terminating decimal to a fraction
Convert 0.75 to a fraction.
There are 2 digits after the decimal point, so 0.75 means 75 hundredths, or 75/100. Both 75 and 100 can be divided by 25. Divide the numerator and denominator by 25: 75 ÷ 25 = 3 and 100 ÷ 25 = 4. So 0.75 = 3/4, which is a fraction.
Example 2 (upper grades): Decide if a fraction has a terminating decimal
Decide whether 7/40 is a terminating decimal when written as a decimal, and then find that decimal.
First, look at the denominator 40. Factor 40 into prime factors: 40 = 2 × 2 × 2 × 5, or 2^3 × 5. Since the only prime factors are 2s and 5s, 7/40 will have a terminating decimal.
Now divide 7 by 40: 7 ÷ 40.
40 does not go into 7, so write 7.000 and think of it as 7.000 ÷ 40. 40 goes into 70 one time, so the first digit is 1 and there is a remainder of 30. Bring down a 0 to make 300. 40 goes into 300 seven times (7 × 40 = 280), with a remainder of 20. Bring down another 0 to make 200. 40 goes into 200 five times (5 × 40 = 200), with no remainder. The division ends, so the decimal terminates at 0.175. Therefore 7/40 = 0.175, a terminating decimal.
Going deeper with terminating decimals
Terminating decimals are one kind of decimal that represent rational numbers, which are numbers that can be written as a fraction of two integers. Every terminating decimal can be turned into a fraction, and every fraction whose denominator (after simplifying) has only 2s and 5s as prime factors will become a terminating decimal.
When your child converts between fractions, decimals, and percents, terminating decimals are often the easiest to work with. For example, 0.2, 0.25, and 0.5 are common terminating decimals that connect to benchmark fractions and percents like 1/5, 1/4, and 1/2.
In later grades, recognizing whether a decimal is terminating or repeating helps your child classify rational numbers and decide how to write answers from division. If a division problem ends with no remainder, the answer is a terminating decimal. If the remainder keeps cycling, the answer is a repeating decimal, which may need to be rounded to a certain place value.
Common mistakes with terminating decimals
- Mistake 1: Thinking any decimal with "a lot" of digits is repeating, not terminating. For example, a student might think 3.1416 is repeating because it has four digits after the decimal. Correction: A decimal is repeating only if a digit or pattern goes on forever; if the digits stop, it is a terminating decimal, no matter how many digits there are.
- Mistake 2: Forgetting place value when turning a terminating decimal into a fraction. A student might write 0.6 as 6/100 instead of 6/10. Correction: The last digit of 0.6 is in the tenths place, so 0.6 means 6 tenths, or 6/10, which can then be simplified to 3/5.
- Mistake 3: Assuming every fraction has a terminating decimal. For example, a student might try to divide 1 by 3 and stop at 0.33, calling it a terminating decimal. Correction: 1/3 has a repeating decimal, 0.333..., because the 3s go on forever; only fractions whose simplified denominators have prime factors of 2 and 5 only will have terminating decimals.
Where terminating decimals show up in everyday life
Terminating decimals appear in prices, measurements, and scores that stop at a certain place. A price of $4.99, a length of 1.25 meters, or a game score of 9.5 points are all terminating decimals. When your child reads money amounts or measurements, they are working with terminating decimals.