There are 2,000 pounds in a ton. How can you write 2,000 with an exponent?
The objective is to express the number \(2,000\) in scientific notation. Scientific notation represents a number in the form \(a \times 10^n\), where \(1 \leq |a| < 10\) and \(n\) is an integer. For the number \(2,000\), we first identify the leading non-zero digit, which is \(2\). We then determine how many powers of ten we need to multiply this digit by to reach the original number.
To convert \(2,000\) into scientific notation, we identify the factor \(a\) and the exponent \(n\). We can write \(2,000\) as the product of \(2\) and \(1,000\). Since \(1,000\) can be expressed as a power of \(10\), specifically \(10 \times 10 \times 10 = 10^3\), we substitute this into our expression. Thus, we have \(2,000 = 2 \times 10^3\). This fits the required format of one non-zero digit multiplied by a power of ten.
By expressing \(2,000\) as \(2 \times 10^3\), we successfully write the number in scientific notation. Therefore, the final answer is \(2 \times 10^3\).
Scientific notation is frequently used in fields like astronomy and physics to handle extremely large or small numbers. For example, the distance from the Earth to the Sun is approximately \(150,000,000\) kilometers, which can be written in scientific notation as \(1.5 \times 10^8\) kilometers. This shorthand makes it much easier to perform calculations and compare values without writing out many trailing zeros.