Virginia SOL 7.NS.1.c
The Standard
Convert between numbers greater than 0 written in scientific notation and decimals.*
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 translate positive values between scientific notation and decimal form. They use the exponent to determine the direction and number of place-value shifts while keeping the digits in order.
What Mastery Looks Like
- Students convert accurately in both directions, including values with many placeholder zeros. They write scientific notation with a coefficient at least 1 but less than 10 and can explain how the exponent controls place value.
Common Misconceptions
- Students often reverse the direction of the decimal shift for positive and negative exponents. They may count digits instead of place-value shifts or omit placeholder zeros. Some write coefficients equal to 10 or less than 1.
How to Assess It
- Exit ticket: Write 0.00072 in scientific notation and write 4.06 × 10^5 in decimal form. Show each place-value shift.
Lesson moves
Ways to Teach It
Use digit cards on a place-value mat as students model 3.42 × 10^4 and 3.42 × 10^-4 by shifting place values.
Have students explain why 6.3 × 10^-5 is smaller than 6.3, then verify their reasoning with a calculator.
Play Conversion Relay with cards showing decimals or scientific notation as teams race to match equivalent values and correct invalid coefficients.
Use a space-distance table and ask students to convert each value, then choose the clearer format for a public information poster.
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Printable 7.NS.1.c Worksheet
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Related Standards
- 7.NS.1.d
Compare and order no more than four numbers greater than 0 written in scientific notation. Ordering may be in ascending or descending order.*
- 4.NS.4.c
Read and write decimals expressed through thousandths, using concrete, pictorial, and numerical representations.
- 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
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...
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