Question

In Problems 129-136, write each number as a decimal. \(6.453 \times 10^{-1}\)

Short answer

0.6453

Step-by-step solution

Identify the base number

The given number is written in scientific notation: \(6.453 \times 10^{-1}\). First, identify the base number which is 6.453.

Understand the exponent

Observe that the exponent of 10 is -1. This indicates the direction and number of places we will move the decimal point.

Move the decimal point

Move the decimal point one place to the left because the exponent is -1. So, moving the decimal point one place to the left from 6.453 results in 0.6453.

Key concepts

Decimal Conversion

Scientific notation is used to express very large or very small numbers conveniently. In the exercise, we need to convert a number from scientific notation to its decimal form. This involves understanding where to place the decimal point. For the given number, \( 6.453 \times 10^{-1} \), the decimal point moves to the left because the exponent of 10 is negative. By moving the decimal point one place to the left, the number becomes 0.6453. This is the decimal conversion of the given scientific notation.

Exponents

Exponents are a key part of scientific notation. An exponent indicates how many times a base number is multiplied by itself. When the exponent is negative, it shows how many times the base number is divided by itself. In the expression \( 10^{-1} \), the exponent -1 means that we divide 10 by 10, resulting in 0.1. Understanding this helps in converting from scientific notation to decimals. Always remember: A positive exponent moves the decimal point to the right, making the number larger, while a negative exponent moves it to the left, making the number smaller.

Base Number

In scientific notation, the base number is the number multiplied by 10 raised to an exponent. In our example of \( 6.453 \times 10^{-1} \), 6.453 is the base number. The role of the base number is to represent the significant digits of the number precisely. It helps in maintaining accuracy without dealing with extremes of large or small numbers directly. The exponent adjusts this base number to suit the required scale, whether smaller or larger. By identifying the base number and interpreting the exponent correctly, converting between scientific notation and decimal form becomes straightforward.