Question

For Exercises \(1-16\), match the power of 10 to its name or use. A. \(10^{-12}\) B. \(10^{-9}\) C. \(10^{-6}\) D. \(10^{-3}\) E. \(10^{3}\) F. \(10^{6}\) G. \(10^{9}\) H. \(10^{12}\) I. \(10^{15}\) Latin for "thousandth"

Short answer

The answer is D. \(10^{-3}\).

Step-by-step solution

Understand the Term 'Latin for thousandth'

The exercise asks for a match between the power of 10 and the term 'Latin for thousandth.' We need to find the Latin prefix that translates to 'thousandth.'

Identify the Correct Latin Term for 'thousandth'

The Latin prefix for 'thousandth' is 'milli.' This prefix corresponds to the power of 10 that represents a fraction of a thousand, specifically one one-thousandth.

Match the Prefix to the Power of 10

'Milli,' meaning one-thousandth, is represented by the power of 10 that is the reciprocal of 1000. Since 1000 is represented by the power of 10 (i.e., \(10^3\)), the reciprocal or one-thousandth is \(10^{-3}\).

Conclusion

Therefore, the power of 10 that is referred to as 'Latin for thousandth' is \(10^{-3}\).

Key concepts

Mathematics

Mathematics is a universal language, essential in various fields for understanding and explaining the world around us. It involves different branches and topics, such as algebra, geometry, calculus, and statistics, to name a few. A fundamental aspect of mathematics is understanding powers of ten. This concept forms the basis for more advanced topics, like scientific notation and decimal prefixes. Understanding each part can help students grasp mathematical ideas more clearly, making problem-solving efficient and effective.

Decimal Prefixes

Decimal prefixes are used to denote multiples or fractions of units in the metric system. These prefixes help easily express large or small numbers without dealing with numerous zeros.
For instance:

• 'Kilo-' means a thousand, or \(10^3\).
• 'Milli-' is used for a thousandth, or \(10^{-3}\).
• 'Micro-' means one millionth, or \(10^{-6}\).

These prefixes provide a convenient way to work with measures and quantities in various scientific and everyday contexts. Recognizing decimal prefixes allows for fluent conversions and a better understanding of quantities.

Scientific Notation

Scientific notation is a way to express very large or very small numbers in a compact form. Instead of writing out long numbers fully, you use a base number and the power of ten.
For example:

• The number 1,000 can be written as \(1 \times 10^3\).
• 0.001 is expressed as \(1 \times 10^{-3}\).

This method is beneficial in fields like science and engineering, where precise and straightforward representation of data is crucial. It simplifies calculations and ensures clarity, especially when dealing with astronomical or microscopic scales.

Fractions

Fractions represent parts of a whole and are expressed as a quotient of two numbers—a numerator and a denominator. In mathematics, fractions are fundamental for understanding division and proportionality. When working with powers of ten, fractions often come into play to denote divisions or multiplications of 100, 1,000, and so on.
For instance, the fraction \(\frac{1}{1000}\) translates to a thousandth, which corresponds to the power \(10^{-3}\). This shows how fractional thinking helps in comprehending decimal prefixes and powers of ten, providing a bridge between different mathematical concepts and practical applications.