# Multiplying Decimals

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Multiplying decimals is similar with multiplying whole numbers. To multiply decimals, we may disregard the decimal points and just treat the decimal number as whole number. Following the rule for multiplying whole numbers, multiply the last digit in the multiplier with every digit in the multiplicand. Then multiply the second digit (from the right) of the multiplier to every digit of the multiplicand but place the first product or the unit digit of the first product one positional value below from the first digit of the first line of products obtained from multiplying the first digit in the multiplier and the digits in the multiplicand. Follow the same rule until all the digits in the multiplier have been multiplied to all the digits in the multiplicand. Add all the partial products by following addition rule for whole numbers. Count the total number of places to the right of the decimal point in the multiplier and in the multiplicand. The number of digits to the right of the decimal point of the product is equal to the number of places in these factors.

Below are examples that illustrate the above rules for multiplying decimals:

Find the product between the given pair of decimal numbers.

1. 2.34 and 13.2
2. 3.105 and 2.12
3. 12.1 and 4.6
4. 2.376 and 0.21

$1.\;\;\; \begin{array}{c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c} & &2&.&3 & 4 \\ \times&1&3&.&2 & \\ \hline &&4&&6 & 8 & \;\textup{multiply 234 by 2}\\ & 7& 0 && 2 &&\;\textup{multiply 234 by 3}\\ 2&3 & 4 &&&&\;\textup{multiply 234 by 1} \\ \hline 3&0. & 8 &&8&8& \;\textup{total number of places to the right}\\ \end{array}$

$2.\;\;\; \begin{array}{c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c} &3 &.&1&0 & 5 \\ \times&&&4&. &6 \\ \hline &1&8&6&3 &0 & \;\textup{multiply 3105 by 6}\\ 1&2&4&2&0&&\;\textup{multiply 3105 by 4}\\ \hline 1&4&.&2&8&3&0 \;\;\textup{total number of places to the right}\\ \end{array}$

$3.\;\;\; \begin{array}{c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c} &1 &2&.&1 & \\ \times&&4&.&6& \\ \hline &7&2&&6&& \;\textup{multiply 121 by 6}\\ 4&8&4&&&&\;\textup{multiply 3105 by 4}\\ \hline 5&5&.&6&6&& \;\;\textup{total number of places to the right}\\ \end{array}$

$4.\;\;\; \begin{array}{c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c@{\,}c} &2&.&3&7&6 \\ \times &&0&.&2&1 \\ \hline &2&&3&7&6& \;\textup{multiply 2376 by 1}\\ 4&7&&5&2&&\;\textup{multiply 2376 by 2}\\ \hline 0.4&9&&8&9&6& \;\;\textup{total number of places to the right}\\ \end{array}$