1.47 10 3 0.860 10 2 Calculator

This calculator helps you multiply numbers in scientific notation. Simply enter the coefficients and exponents, and it will calculate the product in standard form.

How to Use This Calculator

To use this calculator:

Enter the first coefficient (1.47 in the example)
Enter the first exponent (3 in the example)
Enter the second coefficient (0.860 in the example)
Enter the second exponent (2 in the example)
Click "Calculate" to see the result

The calculator will display the product in both scientific notation and standard form.

Formula Explained

When multiplying numbers in scientific notation, you multiply the coefficients and add the exponents:

(a × 10^b) × (c × 10^d) = (a × c) × 10^b+d

For example, multiplying 1.47 × 10³ and 0.860 × 10²:

Multiply the coefficients: 1.47 × 0.860 = 1.2642
Add the exponents: 3 + 2 = 5
Combine to get 1.2642 × 10⁵

This is equivalent to 126,420 in standard form.

Worked Examples

Example 1: Basic Multiplication

Calculate 1.47 × 10³ × 0.860 × 10²:

Multiply coefficients: 1.47 × 0.860 = 1.2642
Add exponents: 3 + 2 = 5
Result: 1.2642 × 10⁵ (or 126,420)

Example 2: Different Exponents

Calculate 2.5 × 10⁴ × 3.1 × 10⁻²:

Multiply coefficients: 2.5 × 3.1 = 7.75
Add exponents: 4 + (-2) = 2
Result: 7.75 × 10² (or 775)

Frequently Asked Questions

What is scientific notation?

Scientific notation is a way of writing very large or very small numbers by expressing them as a product of a number between 1 and 10 and a power of 10. For example, 1,470,000 is written as 1.47 × 10⁶.

How do I multiply numbers in scientific notation?

To multiply numbers in scientific notation, multiply the coefficients and add the exponents. For example, (2 × 10³) × (3 × 10⁴) = (2 × 3) × 10³⁺⁴ = 6 × 10⁷.

What if one of the coefficients is less than 1?

If one of the coefficients is less than 1 (like 0.860), you can still multiply it normally. The result will automatically be in proper scientific notation. For example, 1.47 × 0.860 = 1.2642.