High School Placement Test (HSPT) Practice Test

What is 2,300 in scientific notation?

1. 2.3 × 10^3

2. 2.3 × 10^2

3. 0.23 × 10^4

4. 23 × 10^2

The correct answer is: 2.3 × 10^3

To express the number 2,300 in scientific notation, we want to represent it in the form of \( a \times 10^n \), where \( a \) is a number greater than or equal to 1 and less than 10, and \( n \) is an integer. Starting with 2,300, we can rewrite it in a more manageable form. We observe that we can shift the decimal place to the left two positions to get 2.3. Each time we move the decimal left, we multiply by 10. Because we moved the decimal left two positions, we need to account for this shift by multiplying by \( 10^3 \) (since moving it left from 2.3 gives us 2,300). Thus, we write 2,300 as: \[ 2.3 \times 10^3 \] This meets the requirement of scientific notation, where 2.3 is between 1 and 10, and we have the correct power of ten. The other options either do not maintain the correct placement of the decimal or do not accurately reflect the original number in the context of scientific notation. For instance, the second choice has the base not in the correct