Counting in powers of 10

​​In a nutshell

Counting in powers of $$10$$ involves multiplying a number by $$10$$ over and over, noting down the result each time. 

How to count in powers of 10

When counting in powers of ten, a number is multiplied by $$10$$ repeatedly. How you do this depends on whether your number is a decimal or a whole number.

Count in powers of $$10$$​ for decimal numbers.

Procedure

Note: Zeros to the left of the first digit after the zero do not need to written down under columns greater than the ones.

Example 1

Count in powers of $$10$$ from $$0.072$$ to $$72$$.

The first number after the decimal place that is not zero is seven.

$$\begin{array}{ccccccc} \text{Hundreds} & \text{Tens} & \text{Ones} &.&\text{Tenths} &\text{Hundredths}&\text{Thousandths} \\ & & 0& . & 0 & \boxed7&2\end{array}$$​​

Move the seven (and every digit that follows) one place value to the left.

$$\begin{array}{ccccccc} \text{Hundreds} & \text{Tens} & \text{Ones} &.&\text{Tenths} &\text{Hundredths}&\text{Thousandths} \\ & & 0& . & 0 & \underline7&2\\ & & 0& . & \underline7&2& \\\end{array}$$​​

Repeat until you reach $$72$$.

$$\begin{array}{ccccccc} \text{Hundreds} & \text{Tens} & \text{Ones} &.&\text{Tenths} &\text{Hundredths}&\text{Thousandths} \\ & & 0& . & 0 & \underline7&2\\ & & 0& . & \underline7&2& \\&&\underline7&.&2&&\\&\underline7&2&.&&&\end{array}$$

So from $$0.072$$, counting in powers of $$10$$ we have:

$$\underline{0.072,0.72,7.2,72}$$

Note: To count backwards in powers of ten, do the opposite to the steps above: move every digit one place to right, replacing empty spaces after the decimal place with zeros.

Count in powers of $$10$$​ for whole numbers.

PROCEDURE

Example 2

Count in powers of $$10$$ from $$72$$ to $$7\space200\space000$$.

Move every digit one place to the left and add a zero.

$$\begin{array}{ccccccc}\text{Millions}&\text{Hundred Thousands} &\text{Ten Thousands}&\text{Thousands} & \text{Hundreds} & \text{Tens} & \text{Ones} \\ &&&&&7&2\\&&&&7&2&0\end{array}$$

​

Repeat until you reach $$7\space200\space000$$.

$$\begin{array}{ccccccc}\text{Millions}&\text{Hundred Thousands} &\text{Ten Thousands}&\text{Thousands} & \text{Hundreds} & \text{Tens} & \text{Ones} \\ &&&&&7&2\\&&&&7&2&0\\&&&7&2&0&0\\&&7&2&0&0&0\\&7&2&0&0&0&0\\7&2&0&0&0&0&0\\\end{array}$$

So from  $$72$$ to $$7\space200\space000$$, counting in powers of $$10$$ we have: 

​$$\underline{72,720,7200,72\space000, 720\space000, 7\space200\space000}$$

Note: To count backwards in powers of ten, do the opposite to the steps above: take away a zero and move every digit one place to the right.