Multiplying numbers in scientific notation uses the laws of exponents.

To multiply a two scientific notation, we use the associative and commutative properties to regroup the numbers to multiply.

Associative property tells that you can insert any numbers in the parentheses to multiply first.

(a x b) x c = a x (b x c)

**Example**: (3 x 4) x 2 = 3 x (4 x 2)

Commutative property tells that you can switch the order in which we multiply numbers.

a x b = b x a

**Example**: 6 x 4 = 4 x 6

In Multiplying Numbers with Scientific Notation, a number is said to be written in Scientific notation if it is expressed as b ×10

A number in multiplying scientific notation is printed as the product of a number either it is integer or decimal or it is a power of 10. The numbers have one digit to the left of the decimal point. The decimal of power that ten indicates how many places the decimal point was moved.

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Below you could see steps for scientific notation multiplication

**Step 1**: Multiply the coefficient of the given numbers, and ‘’a’’ and ‘’c’’ to get ‘’ac’’.**Step 2**: Add the number 10 to the power.

**Step 3**: Suppose if the coefficient of the result is greater than 10, then we can write the result in the form of a.c × 10^{(b + d + 1)}^{}
### Solved Examples

**Question 1: **(5 x 10^{2}) x (5 x 10^{3})

** Solution: **

**Question 2: **(1 x 10^{2}) x (2 x 10^{2})

** Solution: **

### Practice Problems

**Question 1: **( 3 x 10^{4} ) ( 2 x 10^{5 })

**Question 2: **( 6 x 10 ^{3} ) (7 x 10^{3 })

**Question 3: **( 2.1 x 10^{ 5} ) ( 7.1 x 10^{ 5} )

**Question 4: **( 6 x 10^{3} )( 5 x 10^{6 })( 4 x 10^{2} )

a × 10^{b} × c × 10^{d}

Result: ac × 10^{(b + d)}

Below are few examples on** **Multiplying Numbers with Scientific Notation:

**Scientific notation:** To obtain the exponent scientific notation calculate the number of places from the decimal to the end of the number.

The term 33,300,000,000,000 there are 11 places.

Therefore can we write the term 33,300,000,000,000 as:

3.33 x 10^{13}

** Example:** 99900000

1) 9.99 x 10^{7}

**Make a note of (a ^{m}. a^{n}) as of the note the example problem have similar base.**

= 25 x 10^{5}

Move the decimal point over to the right until the coefficient lies between 1 and 10.

For each place shift the decimal in excess of the exponent will be lowered 1 power of ten.

25 x 10^{ 5} = 2.5 x 10^{6 }in scientific notation.

= 2 x 10^{4}

= 0.2 x 0^{5}

Move the decimal point over to the right until the coefficient lies between 1 and 10.

For each place shift the decimal in excess of the exponent will be lowered 1 power of ten.

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