Problem 49 - Algebra 1

Question

CALCULATOR Use a calculator to evaluate the expression. Write the result in scientific notation and in decimal form. $$ 0.000279 \cdot 3,940,000,000 $$

Step-by-Step Solution

Answer

The product is 1098.66 in decimal form and \(1.09866 \times 10^{3}\) in scientific notation.

Step 1: Multiply the given numbers

First, multiply the given numbers using a calculator. This gives 0.000279 * 3,940,000,000 = 1098.66

Step 2: Convert to scientific notation

To write this number in scientific notation, the number is converted into a number between 1 and 10 by moving the decimal point to the right, and the exponent shows how many places the decimal was moved. Thus, 1098.66 becomes \(1.09866 \times 10^{3}\)

Key Concepts

Decimal Form

Decimal form is a way to represent numbers using powers of ten. It provides a clear and straightforward way to express both small and large numbers. In the original exercise, decimal form is used to express the result of the multiplication process as 1098.66.

When working with numbers in decimal form:

• Each position of a digit is associated with a power of ten.
• The number to the left of the decimal point represents whole numbers.
• The numbers to the right indicate fractional parts of ten, hundred, and so on.

Understanding decimal form is crucial because it allows you to switch back and forth between it and other forms like scientific notation, which is particularly useful for extremely large or small numbers.

Calculator Usage

Calculators are incredible tools that help us perform mathematical operations quickly and accurately. In problems involving scientific notation or large multipliers, using a calculator can be essential.

To use a calculator effectively:

• Understand the functions your calculator offers, such as multiplication, division, and conversion features.
• Enter numbers carefully to avoid errors, especially when dealing with multiple decimal places.
• Familiarize yourself with using scientific notation mode, it can convert results into scientific notation automatically.

By practicing how to use your calculator efficiently, you can simplify complex math problems and get the required decimal or scientific notation results accurately.

Multiplication

Multiplication is a basic arithmetic operation where a number is added to itself a certain number of times. It can be thought of as repeated addition. In the exercise, the task is to multiply 0.000279 by 3,940,000,000.

Key points about multiplication:

• It is essential in converting smaller units to larger ones (and vice versa), as seen in conversions from scientific notation to decimal form.
• Large number multiplication is easier with a calculator, but understanding the process manually strengthens your mathematical skills.
• Multiplying by powers of ten is simplified when numbers are in decimal form, by simply moving the decimal point.

Strong multiplication skills are fundamental in math and science, helping to solve problems more efficiently whether with or without a calculator.