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Multiplying decimals by whole numbers

Tutor: Alice

# Multiplying decimals by whole numbers

## In a nutshell

Multiplying decimals by whole numbers is very much like multiplying any other pair of numbers together. The only added step is to make sure that the decimal point is added to the  correct column.

## Multiplying by a one-digit number

When multiplying a decimal by a one-digit number, short multiplication can be used, just like when multiplying two whole numbers.

#### procedure

 1 Set out the calculation:Write out the place value columns and a column for the decimal point.Place the decimal's digits in the correct columns and the whole number underneath in the ones column. 2 Multiply each digit of the decimal number by the single digit from right to left.​ 3 Carrying when required, write out the answer in the space below, using the correct place value columns. 4 Add back in the decimal point, positioned directly under the decimal column.

##### Example 1​

What is $1.56\times3$?

Set out the calculation.

$\begin{array}{cccc}& \text{T} & \text{O} &.&\text{Tth} & \text{Hth} \\& & 1 & . &5&6 \\\times & & 3&&& \\ \hline&&&& \\ \hline&&&&\end{array}$​​

Multiply each digit of the decimal by three, carrying as necessary.

$\begin{array}{cccc}& \text{T} & \text{O} &.&\text{Tth} & \text{Hth} \\& & 1 & . &5&6 \\\times & &3 &&& \\ \hline&&4&&6&8 \\ \hline&&^1&&^1&\end{array}$

Add back in the decimal point.

$\begin{array}{cccc}& \text{T} & \text{O} &.&\text{Tth} & \text{Hth} \\& & 1 & . &5&6 \\\times & & 3&&& \\ \hline&&4&.&6&8 \\ \hline&&^1&&^1&\end{array}$

​​

$1.56\times3=\underline{4.68}$

## Multiply by a two-or-more-digit number

The method of multiply a two-or-more-digit number is the same. However, this time, long multiplication is needed.

#### Procedure

 1 Set out the calculation (as before). 2 Multiply each digit of the decimal number by the each digit of the whole number from right to left. 3 Carrying where required, write out the answer to each one below the other in the answer space, using the correct place value columns. 4 Add back in the decimal , positioned directly under the decimal column.​

​​​

##### Example 2

What is $6.32\times32$?

Set out the calculation.

$\begin{array}{cccc}& \text{T} & \text{O} &.&\text{Tth} & \text{Hth} \\& & 6 & . &3&2 \\\times & 3& 2&&& \\ \hline&&&& \\ \hline&&&&\end{array}$​​

Multiply each digit of the decimal by two, carrying where necessary.

$\begin{array}{cccc}&\text{H}& \text{T} & \text{O} &.&\text{Tth} & \text{Hth} \\&& & 6 & . &3&2 \\\times& & 3& 2&&& \\ \hline&&^11&2&&6&4 \\ \\ \hline\end{array}$​​

Add a zero to the hundredths column (to account for the thirty) and multiply each digit of the decimal by three.

$\begin{array}{cccc}&\text{H}& \text{T} & \text{O} &.&\text{Tth} & \text{Hth} \\&& & 6 & . &3&2 \\\times& & 3& 2&&& \\ \hline&&^11&2&&6&4 \\ &^11&8&9&&6&0 \\ \hline\end{array}$​​

$\begin{array}{cccc}&\text{H}& \text{T} & \text{O} &.&\text{Tth} & \text{Hth} \\&& & 6 & . &3&2 \\\times& & 3& 2&&& \\ \hline&&^11&2&.&6&4 \\ &^11&8&9&.&6&0 \\ \hline&^12&^10&^12&.&2&4\end{array}$

​​$6.32\times32=\underline{202.24}$​​

## FAQs - Frequently Asked Questions

### How do I multiply a decimal by a one-digit number?

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