Problem 117 - Algebra A Combined Function

Question

Write each number in standard form. Then write the number in scientific notation. The estimated number of Google users in a day is 0.44 billion.

Step-by-Step Solution

Answer

Standard form: 440,000,000, Scientific notation: \(4.4 \times 10^8\).

Step 1: Convert to Standard Form

The number provided is 0.44 billion. First, we need to express this number in its standard numerical form. Since 1 billion equals 1,000,000,000, we calculate 0.44 times 1,000,000,000: \[ 0.44 \times 1,000,000,000 = 440,000,000. \] Thus, the standard form of the number is 440,000,000.

Step 2: Express in Scientific Notation

To write the number 440,000,000 in scientific notation, we identify the first non-zero digit: 4.4. We count how many places we move the decimal from the end of the number to just after the first digit. That is 8 places to the left. So, \[ 440,000,000 = 4.4 \times 10^{8}. \] Therefore, the scientific notation of the number is \( 4.4 \times 10^{8} \).

Key Concepts

standard form

Standard form refers to the way a number is written using its full digits without abbreviation. For our exercise, we use the example of converting 0.44 billion into standard form. Here's how it's done:

• "Billion" indicates a multiplier of 1,000,000,000, so when you have 0.44 billion, you multiply 0.44 by 1,000,000,000.
• This multiplication results in 440,000,000. Each digit represents part of the whole number without any exponents.

The term 'standard form' is often mistaken with 'scientific notation', but the difference lies in scientific notation expressing a number in terms of a digit and a power of ten, while standard form presents it completely expanded.

decimal conversion

Decimal conversion processes a number from its fractional representation to a standard numeric value. In our example, 0.44 billion is originally a decimal representation of the number of Google users. Here's what happens in the conversion:

• We begin with the decimal 0.44. Decimals express parts of numbers as powers of ten.
• This figure stands for 44% of a billion. By converting, we calculate 0.44 times the standard numeric representation of billion (1,000,000,000).
• The multiplication results in 440,000,000, transitioning the decimal way of expression to standard form.

Understanding decimal conversion is important as it allows us to work across different forms of numerical data, enhancing our ability to communicate and express numbers accurately.

numerical expressions

Numerical expressions involve the articulation of numbers through mathematical operations. This exercise requires recognizing and manipulating numbers to swap between forms like standard and scientific notation. Here's how:

• Starting with 440,000,000, think of it as a numerical expression derived from the operation 0.44 multiplied by a billion.
• This expression fully represents the number, allowing it to be broken down further into various forms.
• By putting 440,000,000 into scientific notation, where it's expressed as 4.4 multiplied by 10 raised to the eighth power, we see another type of numerical expression that simplifies numbers.

Mastering numerical expressions is foundational in mathematics, enabling problem-solving and analysis while handling expansive or minuscule numbers efficiently and succinctly.