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Scientific Notation

Write very large and very small numbers in scientific notation

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Scientific Notation

What is Scientific Notation?

A way to write very large or very small numbers: a×10na \times 10^n

where 1≤∣a∣<101 \leq |a| < 10 and nn is an integer

Large Numbers

Example: 5,600,000=5.6×1065,600,000 = 5.6 \times 10^6

Move decimal left → positive exponent

Small Numbers

Example: 0.0000034=3.4×10−60.0000034 = 3.4 \times 10^{-6}

Move decimal right → negative exponent

Converting to Standard Form

From scientific notation:

  • Positive exponent → move decimal right
  • Negative exponent → move decimal left

Examples:

  • 4.2×103=4,2004.2 \times 10^3 = 4,200
  • 7.8×10−4=0.000787.8 \times 10^{-4} = 0.00078

Operations

Multiplying

Multiply the numbers, add the exponents: (3×104)×(2×105)=6×109(3 \times 10^4) \times (2 \times 10^5) = 6 \times 10^9

Dividing

Divide the numbers, subtract the exponents: 8×1074×103=2×104\frac{8 \times 10^7}{4 \times 10^3} = 2 \times 10^4

📚 Practice Problems

1Problem 1easy

❓ Question:

Write in scientific notation: 47,000

💡 Show Solution

Solution:

Move decimal point 4 places to the left: 47,000=4.7×10447,000 = 4.7 \times 10^4

(Positive exponent because the original number is large)

Answer: 4.7×1044.7 \times 10^4

2Problem 2easy

❓ Question:

Write in scientific notation: 47,000

💡 Show Solution

Solution:

Move decimal point 4 places to the left: 47,000=4.7×10447,000 = 4.7 \times 10^4

(Positive exponent because the original number is large)

Answer: 4.7×1044.7 \times 10^4

3Problem 3medium

❓ Question:

Write in standard form: 3.2×10−53.2 \times 10^{-5}

💡 Show Solution

Solution:

Negative exponent means move decimal 5 places to the left: 3.2×10−5=0.0000323.2 \times 10^{-5} = 0.000032

Answer: 0.0000320.000032

4Problem 4medium

❓ Question:

Write in standard form: 3.2×10−53.2 \times 10^{-5}

💡 Show Solution

Solution:

Negative exponent means move decimal 5 places to the left: 3.2×10−5=0.0000323.2 \times 10^{-5} = 0.000032

Answer: 0.0000320.000032

5Problem 5hard

❓ Question:

Calculate: (6×108)×(4×10−3)(6 \times 10^8) \times (4 \times 10^{-3})

💡 Show Solution

Solution:

Multiply the numbers and add the exponents: (6×4)×108+(−3)(6 \times 4) \times 10^{8+(-3)} =24×105= 24 \times 10^5 =2.4×106= 2.4 \times 10^6

(Adjust to proper scientific notation)

Answer: 2.4×1062.4 \times 10^6

6Problem 6hard

❓ Question:

Calculate: (6×108)×(4×10−3)(6 \times 10^8) \times (4 \times 10^{-3})

💡 Show Solution

Solution:

Multiply the numbers and add the exponents: (6×4)×108+(−3)(6 \times 4) \times 10^{8+(-3)} =24×105= 24 \times 10^5 =2.4×106= 2.4 \times 10^6

(Adjust to proper scientific notation)

Answer: 2.4×1062.4 \times 10^6

Explain using:
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Laws of Exponents
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Integer Exponents
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❓ Frequently Asked Questions

What is Scientific Notation?▾
Write very large and very small numbers in scientific notation
How can I study Scientific Notation effectively?▾
Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Practice with the 6 problems provided, checking solutions as you go. Regular review and active practice are key to retention.
Is this Scientific Notation study guide free?▾
Yes — all study notes, flashcards, and practice problems for Scientific Notation on Study Mondo are free to access. No account is needed.
What course covers Scientific Notation?▾
Scientific Notation is part of the Grade 8 Math course on Study Mondo, specifically in the Exponents and Scientific Notation section. You can explore the full course for more related topics and practice resources.
Are there practice problems for Scientific Notation?▾
Yes, this page includes 6 practice problems with detailed solutions. Each problem includes a step-by-step explanation to help you understand the approach.