Question

In Problems 129-136, write each number as a decimal. \(9.88 \times 10^{-4}\)

Short answer

0.000988

Step-by-step solution

Understand the problem

The problem requires transforming the scientific notation number, given as \(9.88 \times 10^{-4}\), into its decimal form.

Interpret the exponent

The exponent \(10^{-4}\) means the decimal point needs to be moved 4 places to the left.

Move the decimal point

Starting with 9.88, move the decimal point 4 places to the left. The number has 2 digits already, so add two more zeroes in front.

Write the final decimal form

0.000988 is the result of moving the decimal point 4 places to the left in 9.88.

Key concepts

Decimal Conversion

Understanding how to convert numbers from scientific notation to decimal form is a critical skill. Scientific notation is a way to express very large or very small numbers in a compact form. When converting a number like \(9.88 \times 10^{-4}\) to decimal form, you need to follow a few simple steps. Start by identifying the exponent, which tells you how many places to move the decimal point. Here, the exponent is -4, meaning you will move the decimal point 4 places to the left. If necessary, add zeroes to ensure the correct placement of the decimal point. For instance, moving the decimal in 9.88 four places to the left, you get 0.000988. This process simplifies the number and makes it easier to read and understand in its standard form.

Negative Exponents

Negative exponents indicate that the number should be made smaller, which involves moving the decimal point to the left. For example, \(10^{-4}\) means you will move the decimal point 4 places to the left because a negative exponent implies division by a power of ten. To illustrate, in the expression \(9.88 \times 10^{-4}\), the exponent -4 requires moving the decimal from after the 9 to four places left, resulting in the number 0.000988. If you had a positive exponent, like \(10^3\), you would move the decimal point to the right. Remembering this rule helps manage both large and small numbers effectively.

Arithmetical Operations

When working with scientific notation and decimal conversion, you often need to perform arithmetical operations like multiplication and division. These operations follow specific rules when dealing with exponents. For instance, multiplying two numbers in scientific notation involves adding their exponents. Dividing involves subtracting the exponents. Always focus on the exponent when performing such operations. In our example, the task was to convert \(9.88 \times 10^{-4}\), which primarily involved interpreting the exponent and shifting the decimal point appropriately. Understanding these basic arithmetic principles allows you to work with complex numbers more easily and efficiently.