Lesson 2: Representing Numbers Using Powers of 10

Property

A power of 10 can be written in exponential form as $10^n$, where the base is 10 and the exponent $n$ indicates the number of times 10 is used as a factor. The value of the exponent $n$ is equal to the number of zeros in the standard form of the number.

Examples

Property

Any number can be expressed as a product of a coefficient and a power of 10. This form is written as $c \times 10^n$, where $c$ is a number and $n$ is an integer. This is useful for writing very large or very small numbers concisely.

Examples

• To write $4,000$ using a power of 10, we can express it as $4 \times 1,000$, which is $4 \times 10^3$.
• To write $720,000$ using a power of 10, we can express it as $7.2 \times 100,000$, which is $7.2 \times 10^5$.
• To write $0.09$ using a power of 10, we can express it as $9 \times 0.01$, which is $9 \times 10^{-2}$.

Explanation

This skill extends the use of powers of 10 to represent any number, not just the powers of 10 themselves. By multiplying a coefficient (a whole or decimal number) by a power of 10, we can write numbers in a more compact form. This method involves identifying the correct power of 10 that, when multiplied by your chosen coefficient, equals the original number. This concept is the foundation of scientific notation.