Virginia SOL 7.NS.1.b
The Standard
Represent a power of 10 with a negative exponent in fraction and decimal form.
Virginia Standards of Learning for Mathematics · The student will investigate and describe the concept of exponents for powers of ten and compare and order numbers greater than zero written in scientific notation.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students rewrite negative powers of ten as unit fractions and decimals. They use the exponent to determine the denominator and the decimal place.
What Mastery Looks Like
- Students correctly show that 10^-4 equals 1/10,000 and 0.0001. They use place value or reciprocal patterns to justify both forms.
Common Misconceptions
- Students may think a negative exponent makes the value negative. They may write 10^-3 as 0.003 or add the wrong number of zeros.
How to Assess It
- Exit ticket: Write 10^-5 as a fraction and a decimal, then explain what the negative exponent tells you.
Lesson moves
Ways to Teach It
Start at 1 on a place-value mat and move a digit right for each negative exponent, recording fraction and decimal forms.
Ask students to explain why 10^-3 equals 1/1,000, not -1,000, using a pattern of powers of ten.
Give groups cards showing powers, fractions, and decimals, then have them race to build matching sets.
Label metric examples, such as 10^-6 meter, with equivalent fractions and decimals, then identify which measurement is smallest.
Free download
Printable 7.NS.1.b Worksheet
A ready-to-print activity worksheet aligned to 7.NS.1.b, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetKeep exploring
Related Standards
- 6.NS.3.d
Recognize and represent powers of 10 with whole number exponents by examining patterns in place value.
- 4.NS.5.c
Write the decimal and fraction equivalent for a given model (e.g., 1 4 = 0.25 or 0.25 = 1 4 ; 1.25 = 5 4 or 11 4 ; 1.02 = 102 100 or 1 2 100 ).*
- 7.NS.1.a
Investigate and describe powers of 10 with negative exponents by examining patterns.
- 7.NS.1
The student will investigate and describe the concept of exponents for powers of ten and compare and order numbers greater than zero written in scientific notat...
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.