Math Problem Statement

For the following exercises, convert numbers to scientific notation and convert scientific notation to standard form.

Solution

Let's go through the conversions for each question.

Convert to Scientific Notation:

  1. 0.0134
    =1.34×102= 1.34 \times 10^{-2}

  2. 0.0000761
    =7.61×105= 7.61 \times 10^{-5}

  3. 3,400
    =3.4×103= 3.4 \times 10^{3}

  4. 8,980,000
    =8.98×106= 8.98 \times 10^{6}

Convert to Standard Form:

  1. 9.01 × 10^5
    =901,000= 901,000

  2. 3.78 × 10^7
    =37,800,000= 37,800,000

  3. 4.32 × 10^{-3}
    =0.00432= 0.00432

  4. 5.781 × 10^{-5}
    =0.00005781= 0.00005781

Would you like a detailed explanation on any of these conversions?

Here are 5 related questions:

  1. How do you convert a large number like 7,000,000 into scientific notation?
  2. How can you express 5.6×1045.6 \times 10^{-4} in standard form?
  3. What are the benefits of using scientific notation for very large or small numbers?
  4. How do you convert 1.25×1031.25 \times 10^3 to standard form?
  5. What is the difference between positive and negative exponents in scientific notation?

Tip: Scientific notation is very helpful for working with extremely large or small numbers, as it makes calculations simpler and reduces errors when dealing with many zeroes.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Standard Form
Powers of 10
Exponents

Formulas

Scientific Notation: a × 10^n where 1 ≤ a < 10 and n is an integer
Standard Form: Convert a × 10^n back to standard numbers by moving the decimal point n places

Theorems

Basic exponent rules
Scientific notation rules

Suitable Grade Level

Grades 6-8