Math Problem Statement

Rewrite the given numbers in standard scientific notation.

Solution

The task asks to rewrite numbers in scientific notation (standardinė išraiška). Below is the step-by-step conversion for each sub-problem. In scientific notation, a number is expressed as a10na \cdot 10^n where 1a<101 \leq |a| < 10.


Answers:

  1. a) 3510135 \cdot 10^1
    = 3.51023.5 \cdot 10^2

  2. b) 123103123 \cdot 10^3
    = 1.231051.23 \cdot 10^5

  3. c) 500102500 \cdot 10^2
    = 5.01045.0 \cdot 10^4

  4. d) 324800102324800 \cdot 10^2
    = 3.2481073.248 \cdot 10^7

  5. e) 0.81010.8 \cdot 10^1
    = 8.01008.0 \cdot 10^0

  6. f) 0.2071030.207 \cdot 10^3
    = 2.071012.07 \cdot 10^1

  7. g) 0.0251020.025 \cdot 10^2
    = 2.51002.5 \cdot 10^0

  8. h) 0.00051020.0005 \cdot 10^2
    = 5.01025.0 \cdot 10^{-2}

  9. i) 300101300 \cdot 10^1
    = 3.01033.0 \cdot 10^3

  10. j) 521102521 \cdot 10^{-2}
    = 5.211005.21 \cdot 10^0

  11. k) 3610336 \cdot 10^{-3}
    = 3.61023.6 \cdot 10^{-2}

  12. l) 35411063541 \cdot 10^{-6}
    = 3.5411033.541 \cdot 10^{-3}

  13. m) 0.71010.7 \cdot 10^1
    = 7.01007.0 \cdot 10^0

  14. n) 0.0051030.005 \cdot 10^3
    = 5.01005.0 \cdot 10^0

  15. o) 0.0231020.023 \cdot 10^{-2}
    = 2.31042.3 \cdot 10^{-4}

  16. p) 0.03621040.0362 \cdot 10^{-4}
    = 3.621063.62 \cdot 10^{-6}

  17. q) 120103120 \cdot 10^3
    = 1.21051.2 \cdot 10^5

  18. r) 750101750 \cdot 10^{-1}
    = 7.51017.5 \cdot 10^1

  19. s) 0.0251010.025 \cdot 10^{-1}
    = 2.51022.5 \cdot 10^{-2}

  20. t) 0.0081010.008 \cdot 10^{-1}
    = 8.01038.0 \cdot 10^{-3}


Questions:

  1. What is the general rule for converting numbers into scientific notation?
  2. How do negative exponents affect the placement of the decimal in scientific notation?
  3. Can you convert 4510445 \cdot 10^{-4} into proper scientific notation?
  4. How do you handle trailing zeros when converting to scientific form?
  5. What are some common mistakes when working with scientific notation?

Tip:

Always ensure that the coefficient aa in scientific notation is between 11 and 1010 (i.e., 1a<101 \leq |a| < 10).

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Exponents
Decimal Conversion

Formulas

a * 10^n where 1 <= |a| < 10

Theorems

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Suitable Grade Level

Grades 7-9