Everything to learn better...

Home

Maths

Number and place value

Counting in powers of 10

Tutor: Alice

# 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

 1 Choose the first number moving along the place value columns that is not zero. 2 Move that digit (and every digit to the right of it) one place value to the left. 3 Continue until every digit has been moved after the decimal point.

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

 1 Move every digit one place value to the left. 2 Replace the empty place value with a zero and repeat.

##### 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.

## FAQs - Frequently Asked Questions

### How do I count in powers of 10 with whole numbers?

Beta

I'm Vulpy, your AI study buddy! Let's study together.