CCSS.Math.Content.7.NS.A.2d
The Standard
Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use long division to write positive and negative fractions as decimals. They decide whether the decimal ends or repeats and show any repeating digit block clearly.
What Mastery Looks Like
- Students correctly divide the numerator by the denominator, add zeros as needed, and keep track of remainders. They use a bar over repeating digits and recognize that a zero remainder means the decimal terminates.
Common Misconceptions
- Students may divide the denominator by the numerator or misplace the decimal point. They may treat a rounded calculator result as exact, or stop before noticing a repeating remainder. Some think every repeating decimal repeats a single digit.
How to Assess It
- Ask students to convert 5/12 and -7/8 using long division, label each decimal as terminating or repeating, and mark any repeating block.
Lesson moves
Ways to Teach It
Use digit and remainder cards to build the long-division sequence for 5/12, stopping when a remainder repeats.
Have students explain why 2/11 repeats while 3/8 terminates, using the remainders from long division as evidence.
Play Decimal Sort Relay with fraction cards, sorting results into terminating, repeating, and not yet determined after three digits.
Compare fractional prices, such as one-third of $10 and three-eighths of $10, and discuss how stores round repeating amounts.
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Printable 7.NS.A.2d Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.7.NS.A.2d, with an answer key for the teacher on its own page. No account needed.
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Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.5.NF.B.3
Interpreting a fraction as numerator divided by denominator supports using long division to write rational numbers as decimals.
- CCSS.Math.Content.6.NS.B.2
Long division of numerator by denominator relies on the same multi-digit division steps, extended with decimal remainders and repeating patterns.
- CCSS.Math.Content.5.NBT.A.3
Decimal place value and notation to thousandths support interpreting quotients as terminating or repeating decimals.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.8.NS.A.1
Students extend rational decimal patterns from long division to distinguish irrational decimals and rewrite repeating decimals as fractions.
- CCSS.Math.Content.HSA-APR.D.6
Number long division gives the quotient and remainder structure used when rewriting polynomial rational expressions by polynomial division.
Keep exploring
Related Standards
- CCSS.Math.Content.8.NS.A
Know that there are numbers that are not rational, and approximate them by rational numbers.
- CCSS.Math.Content.5.NF.B.7a
Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.
- CCSS.Math.Content.7.NS.A.2b
Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If ...
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