Lesson 6: Fluently multiply multi-digit whole numbers using the standard algorithm and using estimation to check for reasonableness of the product.

Property

A power of 10 can be written in exponential form, $10^n$, where the exponent $n$ indicates the number of zeros that follow the 1.
This is equivalent to multiplying 10 by itself $n$ times: $10^n = \underbrace{10 \times 10 \times \dots \times 10}_{n \text{ times}}$.

Examples

Property

To estimate the product of two numbers, round each factor to a nearby, easy-to-multiply number (like its greatest place value). The calculated product should be close to this estimate. If $A \approx A_{est}$ and $B \approx B_{est}$, then the exact product $A \times B$ should be reasonably close to the estimated product $A_{est} \times B_{est}$.

Examples

Property

The standard algorithm for multiplication is a procedure for multiplying numbers by breaking the problem into partial products.

You multiply the top factor by each digit of the bottom factor, one at a time from right to left, and then add the resulting partial products together.