Estimate Quantities with Single Digits and Powers of Ten

A way of expressing numbers as a product of a single digit (1-9) and a power of ten, e.g., $$a \times 10^n$$ .

Identify the leading digit and its place value, then express it as $$d \times 10^n$$ where d is the leading digit and n is the number of places to the right of the decimal.

$$2 \times 10^8$$ .

$$7 \times 10^5$$ .

$$2 \times 10^6$$ .

Identify the first non-zero digit and express it as $$d \times 10^{-n}$$ where d is the digit and n is the number of places to the right of the decimal.

$$2 \times 10^{-4}$$ .

$$6 \times 10^{-5}$$ .

To simplify calculations and make it easier to understand the scale of large or small numbers.

The number of places the decimal point is moved; positive for large numbers and negative for small numbers.