Math Problem Statement

Tuliskan bentuk baku dari bilangan berikut dan tuliskan bentuk bilangan biasa dari bilangan berikut.

Solution

Let's break down the tasks from the image:

  1. First Column: Convert to Standard Form (Bentuk Baku)

      1. 12×10512 \times 10^5
      1. 123×107123 \times 10^{-7}
      1. 4567×1064567 \times 10^6
      1. 6.780.0006.780.000
      1. 78.000.000.00078.000.000.000
      1. 0,0006780,000678
      1. 0,000000000780,00000000078
  2. Second Column: Convert to Regular Form (Bentuk Bilangan Biasa)

    • 8. 5.5005.500
      1. 79.99979.999
      1. 150.000.000150.000.000
      1. 9.876.000.000.0009.876.000.000.000
      1. 0,0077770,007777
      1. 0,000000123-0,000000123
      1. 0,0000000007650,000000000765

Let’s proceed with the conversions:

First Column (Convert to Standard Form):

  1. 12×105=1.2×10612 \times 10^5 = 1.2 \times 10^6
  2. 123×107=1.23×105123 \times 10^{-7} = 1.23 \times 10^{-5}
  3. 4567×106=4.567×1094567 \times 10^6 = 4.567 \times 10^9
  4. 6.780.000=6.78×1066.780.000 = 6.78 \times 10^6
  5. 78.000.000.000=7.8×101078.000.000.000 = 7.8 \times 10^{10}
  6. 0,000678=6.78×1040,000678 = 6.78 \times 10^{-4}
  7. 0,00000000078=7.8×10100,00000000078 = 7.8 \times 10^{-10}

Second Column (Convert to Regular Form):

  1. 5.500=5.5×1035.500 = 5.5 \times 10^3
  2. 79.999=7.9999×10479.999 = 7.9999 \times 10^4
  3. 150.000.000=1.5×108150.000.000 = 1.5 \times 10^8
  4. 9.876.000.000.000=9.876×10129.876.000.000.000 = 9.876 \times 10^{12}
  5. 0,007777=7.777×1030,007777 = 7.777 \times 10^{-3}
  6. 0,000000123=1.23×107-0,000000123 = -1.23 \times 10^{-7}
  7. 0,000000000765=7.65×10100,000000000765 = 7.65 \times 10^{-10}

Would you like further details on any of the conversions, or have any specific questions?

Here are some related questions to further explore the concept:

  1. How do you convert between standard form and regular notation?
  2. What is the importance of scientific notation in practical applications?
  3. How do negative exponents affect the conversion process?
  4. What are the common mistakes when dealing with powers of ten?
  5. How would you approach very large or very small numbers in scientific fields?

Tip: Always double-check your exponent when converting between forms to ensure the decimal is placed correctly.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Standard Form Conversion
Decimal Representation

Formulas

Scientific notation: a × 10^n, where 1 ≤ |a| < 10 and n is an integer
Standard form involves expressing a large or small number in the form of a × 10^n

Theorems

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Suitable Grade Level

Grade 9