# Multiplication Of Decimals

In this section you will learn multiplication of decimals.In our day-to-day life, we come across many situations where we need to know the multiplication of decimal. For example, if money paid in dollars and cents (rupees and paise ), vegetables purchased in kg (kilogram) and g(gram) etc.

**Multiplying decimal by 10,100, 1000 etc.**

**Rule 1 :**On multiplying a decimal by 10, the decimal point is shifted to the right by one place.

**Rule 2 :**On multiplying a decimal by 100, the decimal point is shifted to the right by two places.

**Rule 3 :**On multiplying a decimal by 1000, the decimal is shifted to the right by three places, and so on.

**Multiplication of a decimal by a whole number**

In order to multiply a decimal by a whole number, we follow the following steps :

**Step 1 :**Multiply the decimal without the decimal point by the given whole number.

**Step 2 :**Mark the decimal point in the product to have as many places of decimal as are there in the given decimal.

**Examples :**

1) 3.25 x 12 = ? 325 x 12 ------------ 650 + 3250 ------------ 3900 ∴ 3.25 x 12 = 39.00 (as there are two digits after decimal so from left side count two digits and give the decimal) |
2) 0.0275 x 17 = ? 0.0275 x 17 ------------ 1925 + 2750 ------------ 4675 ∴ 0.0275 x 17 = 0.4675 (as there are 4 digits after decimal so from left side count 4 digits and give the decimal) |

**Multiplication of a decimal by another decimal**

In order to multiply a decimal by another decimal, we follow the following steps.

**Step 1 :**Multiply the two decimals without decimal point just like the whole numbers.

**Step 2 :**Insert the decimal point in the product by counting as many places from the right to left as the sum of the number of decimal places of the given decimals.

**Examples :**

1) 9.2 x 6.07 = ? 9.2 (1 digit after decimal)x 6.07 (2 digits after decimal)------------ 644 000 + 55200 ------------ 55844 (total digits after decimal = 1 + 2 = 3)∴ 9.2 x 6.07 = 55.844 (Total digits after decimal are 3 so from left side count three digits and give the decimal) |
2) 0.0345 x 0.0237 = ? 0.0345 (4 digit after decimal)x 0.0237 (4 digits after decimal)------------ 2415 10350 + 69000 ------------ 81765 (total digits after decimal = 4 + 4 = 8)∴ 0.0345 x 0.0237 = 0.00081765 (Total digits after decimal are 8 but after multiplication there are only 5 digits so add 3 zeros before 8 and then put the decimal 8 digits from left) |

**Introduction of Decimals**

• Expansion of decimals

• Comparison of decimals

• Addition of Decimals

• Subtraction of Decimals

• Multiplication of Decimals

• Division of Decimals

• Conversion of decimals to fraction

Number System

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