Which number in each of the following pairs is larger?a. 7.2 x 10³ or 8.2 x 10²

Verified step by step guidance

1. Step 1: Identify the numbers in scientific notation: 7.2 \times 10^3 and 8.2 \times 10^2.
2. Step 2: Compare the exponents of 10 in each number. The first number has an exponent of 3, and the second number has an exponent of 2.
3. Step 3: Recognize that a larger exponent indicates a larger number when the base (10) is the same.
4. Step 4: Since 10^3 is greater than 10^2, 7.2 \times 10^3 is larger than 8.2 \times 10^2.
5. Step 5: Conclude that 7.2 \times 10^3 is the larger number in the pair.

Key Concepts

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is represented as a product of a number between 1 and 10 and a power of ten. For example, 7.2 x 10³ means 7.2 multiplied by 1000, which simplifies calculations and comparisons of large numbers.

Comparing Exponents

When comparing numbers in scientific notation, the exponent of ten plays a crucial role. The number with the larger exponent is generally larger, as it indicates a greater scale. In the given pairs, 10³ (1000) is larger than 10² (100), which suggests that the number with the higher exponent will likely be larger, provided the coefficients are comparable.

Coefficient Comparison

If two numbers in scientific notation have the same exponent, the coefficients (the numbers in front) must be compared to determine which is larger. In this case, if both numbers had the same power of ten, the larger coefficient would indicate the larger overall number. Thus, understanding how to compare coefficients is essential for accurate evaluation.