Math Problem Statement

Work out (4 × 10^512) ÷ (1.6 × 10^700). Give your answer in standard form.

Solution

Let’s solve the given problem step by step.

We are tasked to calculate:

4×105121.6×10700\frac{4 \times 10^{512}}{1.6 \times 10^{700}}

Step 1: Simplify the constants (4 ÷ 1.6)

4÷1.6=2.54 \div 1.6 = 2.5

Step 2: Simplify the powers of 10

Using the rule of exponents: 1051210700=10512700=10188\frac{10^{512}}{10^{700}} = 10^{512 - 700} = 10^{-188}

Step 3: Combine the results

Now combine the simplified constant with the power of 10: 2.5×101882.5 \times 10^{-188}

Step 4: Ensure the answer is in standard form

The answer is already in standard form: 2.5×10188\boxed{2.5 \times 10^{-188}}

Would you like a detailed explanation of any step?


5 Related Questions:

  1. How do you divide numbers in scientific notation in general?
  2. What are the rules for simplifying powers of 10 during division?
  3. How do you multiply numbers in standard form?
  4. What is the importance of standard form in scientific computations?
  5. Can you provide an example where the exponents result in a positive power after division?

Tip:

When dividing or multiplying numbers in scientific notation, always handle the constants and exponents separately to avoid confusion!

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Exponent Rules
Division in Standard Form

Formulas

a × 10^m ÷ b × 10^n = (a ÷ b) × 10^(m-n)

Theorems

Exponent Rule for Division

Suitable Grade Level

Grades 9-12