Math Problem Statement

Convert numbers between scientific notation and standard notation, including measurements, population data, physics, and more.

Solution

Let's solve the questions from the image one by one.

1. Measurement

  • Given: 25.4 millimeters
  • Task: Write this number in scientific notation.
  • Solution: 25.4 millimeters=2.54×101 millimeters25.4 \text{ millimeters} = 2.54 \times 10^1 \text{ millimeters}

2. Population

  • Given: Population of Rahway, New Jersey, was 26,500.
  • Task: Write this number in scientific notation.
  • Solution: 26,500=2.65×10426,500 = 2.65 \times 10^4

3. Measurement

  • Given: One nanometer is 1.0×1091.0 \times 10^{-9} meters.
  • Task: Write this number in standard notation.
  • Solution: 1.0×109 meters=0.000000001 meters1.0 \times 10^{-9} \text{ meters} = 0.000000001 \text{ meters}

4. Physics

  • Given: The speed of light is about 1.86×1051.86 \times 10^5 miles per second.
  • Task: Write this number in standard notation.
  • Solution: 1.86×105 miles per second=186,000 miles per second1.86 \times 10^5 \text{ miles per second} = 186,000 \text{ miles per second}

5. Computers

  • Given: A CD can store about 650,000,000 bytes of data.
  • Task: Write this number in scientific notation.
  • Solution: 650,000,000 bytes=6.5×108 bytes650,000,000 \text{ bytes} = 6.5 \times 10^8 \text{ bytes}

6. Space

  • Given: The diameter of the Sun is about 1.39×1091.39 \times 10^9 meters.
  • Task: Write this number in standard notation.
  • Solution: 1.39×109 meters=1,390,000,000 meters1.39 \times 10^9 \text{ meters} = 1,390,000,000 \text{ meters}

7. Biology

  • Given: The diameter of a certain virus is 0.0000000280.000000028 meters.
  • Task: Write this number in scientific notation.
  • Solution: 0.000000028 meters=2.8×108 meters0.000000028 \text{ meters} = 2.8 \times 10^{-8} \text{ meters}

8. Mass

  • Given: The mass of planet Earth is about 5.98×10245.98 \times 10^{24} kilograms.
  • Task: Write this number in standard notation.
  • Solution: 5.98×1024 kilograms=5,980,000,000,000,000,000,000,000 kilograms5.98 \times 10^{24} \text{ kilograms} = 5,980,000,000,000,000,000,000,000 \text{ kilograms}

Would you like more details on any of these solutions, or do you have any questions?

Here are five related questions for further practice:

  1. Convert 3.45×1023.45 \times 10^2 to standard notation.
  2. Write 0.00000750.0000075 in scientific notation.
  3. What is 6.022×10236.022 \times 10^{23} written in standard notation?
  4. Convert 4.67×1034.67 \times 10^{-3} to standard notation.
  5. Write 7,890,0007,890,000 in scientific notation.

Tip: Remember, scientific notation is especially useful for expressing very large or very small numbers in a more manageable form.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Standard Notation
Measurement Units

Formulas

Scientific notation: a × 10^n
Standard notation: Expand the number based on the exponent

Theorems

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Suitable Grade Level

Grades 7-9