Math Problem Statement

Express the following numbers as powers of 10: a) 10,000 b) 1/100 c) 10,000² d) 0.01 e) 0.001 f) 1,000,000 g) 1/10,000 h) 0.00001

Solution

The problem asks to express the given numbers as powers of 10. Let's go through each one:

  1. 10 00010 \, 000 = 10410^4
  2. 1100\frac{1}{100} = 10−210^{-2}
  3. 10 000210 \, 000^2 = 10810^8
  4. 0.010.01 = 10−210^{-2}
  5. 0.0010.001 = 10−310^{-3}
  6. 1 000 0001 \, 000 \, 000 = 10610^6
  7. 110 000\frac{1}{10 \, 000} = 10−410^{-4}
  8. 0.000010.00001 = 10−510^{-5}

Would you like a detailed explanation of how each number was converted into a power of 10?

Here are 5 questions to further practice powers of 10:

  1. What is 0.00010.0001 expressed as a power of 10?
  2. Convert 10710^7 to a decimal form.
  3. How would you express 11 000 000\frac{1}{1 \, 000 \, 000} using a power of 10?
  4. Express 1 0001 \, 000 in scientific notation.
  5. If 10−310^{-3} is multiplied by 10210^2, what is the result?

Tip: Remember, every decimal place shift to the right lowers the power of 10 by 1, and every shift to the left increases it by 1.

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Math Problem Analysis

Mathematical Concepts

Powers of 10
Scientific Notation
Exponents

Formulas

10^n, where n is the exponent representing the number of zeros after 1 or the decimal place shifts
Negative exponents represent fractions of 10 (e.g., 10^-2 = 1/100)

Theorems

Exponentiation rules: a^m * a^n = a^(m+n) and a^(-n) = 1/a^n

Suitable Grade Level

Grades 6-8

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