Grade 8 · Real Numbers & Exponents · MAT-08-NS-009
Convert Between Standard and Scientific Notation
Represent and solve convert between standard and scientific notation problems using precise mathematical notation, multiple representations, and justified reasoning.
Learning objectives
What you should be able to do
- Represent and solve convert between standard and scientific notation problems using precise mathematical notation, multiple representations, and justified reasoning.
- Interpret and verify convert between standard and scientific notation results in context, including units, constraints, and reasonableness.
Prerequisite check
Make sure the foundation is ready.
Grade 8 uses this prerequisite as active knowledge in a more formal representation.
Learn
Build the idea from meaning, not memorization.
Meaning and structure
Convert Between Standard and Scientific Notation belongs to real numbers & exponents. Identify the governing property or relationship before choosing a procedure.
Multiple representations
Represent convert between standard and scientific notation numerically and symbolically, then connect it to the Grade 8 Math Box. Tables, graphs, equations, coordinate models, diagrams, and verbal descriptions must agree.
Verification and interpretation
Check with substitution, an inverse operation, an equivalent representation, geometric invariants, estimation, or context. State whether the result is exact or approximate and preserve relevant units and constraints.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Scientific Notation Lab
Keep the coefficient between 1 and 10 while changing the power of ten.
- Model convert between standard and scientific notation in the Math Box.
- Change one input and predict which quantities or invariants should change.
- Explain what the visual, equation, and numerical result say about the same relationship.
Worked examples
Twenty different ways to see the concept work.
Write 120 in scientific notation.
1.2 × 10^2Move the decimal until the coefficient is at least 1 but less than 10.
Write 1300 in scientific notation.
1.3 × 10^3Move the decimal until the coefficient is at least 1 but less than 10.
Write 14000 in scientific notation.
1.4 × 10^4Move the decimal until the coefficient is at least 1 but less than 10.
Write 150000 in scientific notation.
1.5 × 10^5Move the decimal until the coefficient is at least 1 but less than 10.
Write 1600000 in scientific notation.
1.6 × 10^6Move the decimal until the coefficient is at least 1 but less than 10.
Write 17000000 in scientific notation.
1.7 × 10^7Move the decimal until the coefficient is at least 1 but less than 10.
Write 180 in scientific notation.
1.8 × 10^2Move the decimal until the coefficient is at least 1 but less than 10.
Write 1900 in scientific notation.
1.9 × 10^3Move the decimal until the coefficient is at least 1 but less than 10.
Write 20000 in scientific notation.
2.0 × 10^4Move the decimal until the coefficient is at least 1 but less than 10.
Write 210000 in scientific notation.
2.1 × 10^5Move the decimal until the coefficient is at least 1 but less than 10.
Write 2200000 in scientific notation.
2.2 × 10^6Move the decimal until the coefficient is at least 1 but less than 10.
Write 23000000 in scientific notation.
2.3 × 10^7Move the decimal until the coefficient is at least 1 but less than 10.
Write 240 in scientific notation.
2.4 × 10^2Move the decimal until the coefficient is at least 1 but less than 10.
Write 2500 in scientific notation.
2.5 × 10^3Move the decimal until the coefficient is at least 1 but less than 10.
Write 26000 in scientific notation.
2.6 × 10^4Move the decimal until the coefficient is at least 1 but less than 10.
Write 270000 in scientific notation.
2.7 × 10^5Move the decimal until the coefficient is at least 1 but less than 10.
Write 2800000 in scientific notation.
2.8 × 10^6Move the decimal until the coefficient is at least 1 but less than 10.
Write 29000000 in scientific notation.
2.9 × 10^7Move the decimal until the coefficient is at least 1 but less than 10.
Write 300 in scientific notation.
3.0 × 10^2Move the decimal until the coefficient is at least 1 but less than 10.
Write 3100 in scientific notation.
3.1 × 10^3Move the decimal until the coefficient is at least 1 but less than 10.
Practice
Guided practice with hints
01Write 32000 in scientific notation.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: 3.2 × 10^4
02Write 330000 in scientific notation.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: 3.3 × 10^5
03Write 3400000 in scientific notation.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: 3.4 × 10^6
04Write 35000000 in scientific notation.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: 3.5 × 10^7
05Write 360 in scientific notation.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: 3.6 × 10^2
06Write 3700 in scientific notation.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: 3.7 × 10^3
Practice
Independent practice
01Write 38000 in scientific notation.
Answer: 3.8 × 10^4
02Write 390000 in scientific notation.
Answer: 3.9 × 10^5
03Write 4000000 in scientific notation.
Answer: 4.0 × 10^6
04Write 41000000 in scientific notation.
Answer: 4.1 × 10^7
05Write 420 in scientific notation.
Answer: 4.2 × 10^2
06Write 4300 in scientific notation.
Answer: 4.3 × 10^3
07Write 44000 in scientific notation.
Answer: 4.4 × 10^4
08Write 450000 in scientific notation.
Answer: 4.5 × 10^5
Common mistakes
Learn to catch the error, not just the answer.
Repeating nonterminating decimals are rational.
Product and quotient exponent rules require the same base and multiplication or division.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Represent extremely large and small measurements with scientific notation.
- Approximate roots and irrational quantities when decimal estimates are needed.
Challenge problems
Write 4600000 in scientific notation.
4.6 × 10^6
Write 47000000 in scientific notation.
4.7 × 10^7
Write 480 in scientific notation.
4.8 × 10^2
Write 4900 in scientific notation.
4.9 × 10^3
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 8 Algebra & Modeling Sprint
Solve convert between standard and scientific notation problems and justify each result with a valid verification method.
Practice
Mastery check
01Write 50000 in scientific notation.
Answer: 5.0 × 10^4
02Write 510000 in scientific notation.
Answer: 5.1 × 10^5
03Write 5200000 in scientific notation.
Answer: 5.2 × 10^6
04Write 53000000 in scientific notation.
Answer: 5.3 × 10^7
05Write 540 in scientific notation.
Answer: 5.4 × 10^2
06Write 5500 in scientific notation.
Answer: 5.5 × 10^3
07Write 56000 in scientific notation.
Answer: 5.6 × 10^4
08Write 570000 in scientific notation.
Answer: 5.7 × 10^5
Terminology
Words to know
- rational number
- A real number expressible as a ratio of integers with nonzero denominator.
- irrational number
- A real number that cannot be written as a ratio of integers.
- exponent
- A number indicating repeated multiplication by a base.
- scientific notation
- A representation a × 10^n where 1 ≤ |a| < 10 and n is an integer.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Grade 8 instructional guidance, mathematical practices, modeling, and progression toward high-school mathematics.Common Core State Standards for Mathematics — Grade 8
Grade-level expectations for real numbers, equations, functions, geometry, and statistics.Principles to Actions: Ensuring Mathematical Success for All
Research-informed emphasis on reasoning, representations, discourse, productive struggle, and conceptual understanding.