Question 1 of 3Grade 8 State TestNY-8.EE.1Grade 8 Mathematics · Spring 2022 · Q35Non-calculatorproficient
Which expression is equivalent to 4⁻⁵ × 4⁸?
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Unit 2 · Exponents & Scientific Notation
Scientific Notation
A number is in scientific notation when it is a × 10^n with 1 ≤ |a| < 10 and n an integer.
NY-8.EE.3NY-8.EE.4
Notes
Moving the decimal
If you move the decimal left, n is positive (large numbers). If you move it right, n is negative (small numbers). When multiplying, multiply the decimals and add the exponents, then restore 1 ≤ |a| < 10.
Vocabulary
scientific notation
A × 10^n where 1 ≤ |A| < 10 and n is an integer.
Example: The mass of Earth is about 5.97 × 10^24 kg.
Worked examples
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Multiply
(3.0 × 10^4)(2.5 × 10^(−2))
Common errors
Watch for
Writing 35.0 × 10^3 and calling it scientific notation
The leading factor must be at least 1 and less than 10.
Fix: Rewrite as 3.50 × 10^4.
Explore with an applet
Guided practice
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Question 2 of 3Grade 8 State TestNY-8.EE.1Grade 8 Mathematics · Spring 2023 · Q15Non-calculatorproficient
Which expression has a value of 1/16?
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Question 3 of 3Algebra I RegentsAI-N.RN.1Algebra I Regents · June 2024 · Q3Non-calculatoremerging
Which equation is always true?
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Intervention
Place-value chart: each move of the decimal is one power of ten.
Enrichment
Compare 4.2 × 10^7 with 6.1 × 10^6 by converting both to the same power.
Explain your reasoning
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- The exponent is negative because the original number is…