Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for 7th grade rational numbers? Then this Grade 7 lesson on Fractions, Decimals and Rational Number Word Problems explains each idea step by step, with worked examples.
Quick answer: Every rational number can be written as a decimal by dividing the numerator by the denominator. The decimal either terminates, like 38 = 0.375, or repeats a block of digits forever, like 56 = 0.83̅. Word problems with rational numbers use the same sign rules as integers, applied to fractions and decimals.
Standards: 7.NS.A.2d, 7.NS.A.3 · Level: Grade 7
How do you change a fraction into a decimal?
A fraction is a division problem in disguise: the fraction bar means “divided by.” To convert, divide the numerator by the denominator with long division, attaching zeros after the decimal point whenever you run out of digits.
Every rational number is a decimal that either terminates (a remainder of 0 appears) or repeats (a block of digits cycles forever). A bar marks the repeating block: 0.8333… = 0.83̅.
How can you predict whether a decimal stops or repeats?
Write the fraction in lowest terms and factor the denominator. If the only prime factors are 2 and 5, the decimal terminates. Any other prime factor forces a repeat, because only a limited number of remainders exist, so one must eventually return.
| Fraction | Denominator factors | Decimal | Type |
|---|---|---|---|
| 720 | 2 · 2 · 5 | 0.35 | terminates |
| 56 | 2 · 3 | 0.83̅ | repeats |
| 411 | 11 | 0.3̅6̅ | repeats |
912 has a 3 hiding in the denominator, yet in lowest terms it is 34 = 0.75, which terminates. Always simplify before you factor.
How do you solve real-world problems with rational numbers?
- Choose one form, all decimals or all fractions, and write each phrase as an addition, subtraction, multiplication or division.
- Apply the sign rules: same signs add the sizes, different signs subtract the smaller size from the larger and keep the sign of the larger.
- Compute, then compare with a quick estimate.
- Answer in a sentence with units.
A diver at −42.5 ft rises 17.75 ft, then sinks 638 ft. Where is the diver now?
638 = 6.375, so −42.5 + 17.75 − 6.375 = −24.75 − 6.375 = −31.125 ft
Estimate first: −42 + 18 − 6 is about −30, so −31.125 passes the sniff test.
- A fraction means numerator ÷ denominator, so long division converts it to a decimal.
- A decimal terminates when the reduced denominator has only the prime factors 2 and 5.
- All other reduced denominators give repeating decimals, marked with a bar over the repeating block.
- Subtracting a negative number is the same as adding its opposite, for fractions and decimals alike.
Fractions, Decimals and Rational Number Word Problems: frequently asked questions
Is a repeating decimal a rational number?
Yes. Any decimal that terminates or repeats equals a fraction of two integers, so it is rational. Decimals that never repeat and never end, such as π, are not rational.
Why does long division of a fraction always end or repeat?
Each step leaves a remainder smaller than the divisor, so only a limited list of remainders is possible. A remainder of 0 ends the decimal, and a repeated remainder starts the cycle again.
Is 0.999… equal to 1?
Yes. Since 1/3 = 0.333…, multiplying both sides by 3 gives 1 = 0.999…. The two names describe the same point on the number line.
Should I use fractions or decimals in a word problem?
Use whichever form makes the arithmetic easier and keep it consistent. Fractions with repeating decimals, like 1/3, are usually safer as fractions until the final step.
How do I know the sign of a product or quotient?
Same signs give a positive result and different signs give a negative result. Count the negative factors: an even count is positive, an odd count is negative.
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