Math Problem Statement

Solve the given scientific notation division problems.

Solution

Let's go through each of the expressions and solve them step by step using the division rule for scientific notation:

A×10mB×10n=AB×10mn\frac{A \times 10^m}{B \times 10^n} = \frac{A}{B} \times 10^{m-n}

Solutions:

  1. 8×108÷2×1048 \times 10^8 \div 2 \times 10^4
    82×1084=4×104\frac{8}{2} \times 10^{8-4} = 4 \times 10^4

  2. 8×1012÷8×1098 \times 10^{12} \div 8 \times 10^9
    88×10129=1×103\frac{8}{8} \times 10^{12-9} = 1 \times 10^3

  3. 9×106÷3×1039 \times 10^6 \div 3 \times 10^3
    93×1063=3×103\frac{9}{3} \times 10^{6-3} = 3 \times 10^3

  4. 5×108÷1×1045 \times 10^{-8} \div 1 \times 10^{-4}
    51×108(4)=5×104\frac{5}{1} \times 10^{-8 - (-4)} = 5 \times 10^{-4}

  5. 6×107÷2×1026 \times 10^{-7} \div 2 \times 10^{-2}
    62×107(2)=3×105\frac{6}{2} \times 10^{-7 - (-2)} = 3 \times 10^{-5}

  6. 1×106÷2×1031 \times 10^6 \div 2 \times 10^3
    12×1063=0.5×103\frac{1}{2} \times 10^{6-3} = 0.5 \times 10^3 Alternatively, writing in proper scientific notation:
    5×1025 \times 10^2


Would you like a detailed explanation for any of the steps?

Here are 5 related questions to expand your understanding:

  1. How do you convert a number into scientific notation?
  2. What is the difference between multiplying and dividing numbers in scientific notation?
  3. Why do we subtract exponents when dividing powers of ten?
  4. How would you handle division if the coefficients (A and B) resulted in a decimal?
  5. Can you rewrite 0.5×1030.5 \times 10^3 in standard form?

Tip: When dealing with negative exponents, remember that 10n10^{-n} means "1 divided by 10n10^n."

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Scientific Notation
Exponent Rules
Division of Exponents

Formulas

(A × 10^m) ÷ (B × 10^n) = (A/B) × 10^(m-n)

Theorems

Laws of Exponents

Suitable Grade Level

Grades 8-10