x(1.5x10%5E-2)-in-standard-form.jpeg "(2.3x10^4)x(1.5x10^-2) In Standard Form")
Simplifying Scientific Notation: (2.3 x 10⁴) x (1.5 x 10⁻²)
This article will guide you through simplifying the multiplication of two numbers expressed in scientific notation: (2.3 x 10⁴) x (1.5 x 10⁻²).
Understanding Scientific Notation
Scientific notation is a way to express very large or very small numbers in a concise and convenient form. It uses a coefficient multiplied by a power of ten.
For example:
- 2.3 x 10⁴ represents 2.3 multiplied by 10 to the power of 4, which is equivalent to 23,000.
- 1.5 x 10⁻² represents 1.5 multiplied by 10 to the power of -2, which is equivalent to 0.015.
Multiplying Numbers in Scientific Notation
To multiply numbers in scientific notation, we follow these steps:
- Multiply the coefficients: 2.3 x 1.5 = 3.45
- Multiply the powers of ten: 10⁴ x 10⁻² = 10²
- Combine the results: 3.45 x 10²
Expressing in Standard Form
The result, 3.45 x 10², is in scientific notation. To convert this to standard form, we move the decimal point two places to the right (because the exponent is positive two).
Therefore, (2.3 x 10⁴) x (1.5 x 10⁻²) is equal to 345 in standard form.