Multiplication and division - HiSet: High School Equivalency Test: Math

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Question

Multiply, and express the product in scientific notation:

$7,200,000 \times 5,000,000$

Answer

Convert 7,200,000 to scientific notation as follows:

Move the (implied) decimal point until it is immediately after the first nonzero digit (the 7). This required moving the point six units to the left:

$7,200,000. \Rightarrow 7.200000$

It follows that 7,200,000 can be rewritten as $7.2 \times 10^{6}$ .

By similar reasoning, 5,000,000 can be rewritten as $5 \times 10^{6}$ .

Thus,

$7,200,000 \times 5,000,000$

$= (7.2\times 10 ^{6} )\times (5 \times 10^{6} )$

Rearrange and regroup the expressions so that the powers of ten are together:

$= (7.2\times 5) \times (10 ^{6} \times 10^{6} )$

Multiply the numbers in front. Also, multiply the powers of ten by adding exponents:

$= 36 \times 10 ^{6+6}$

$= 36 \times 10 ^{12}$

In order for the number to be in scientific notation, the number in front must be between 1 and 10. An adjustment must be made by moving the implied decimal point in 36 one unit left. It follows that

$36 = 3.6 \times 10^{1}$

Therefore,

$36 \times 10 ^{12} = (3.6 \times 10^{1}) \times 10 ^{12}$

$= 3.6 \times 10^{1+12}$

$= 3.6 \times 10^{13}$ ,

the correct response.

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Question

Multiply:

$5,000,000 \times 120,000,000$

Express the product in scientific notation.

Answer

Scientific notation refers to a number expressed in the form

$\pm a \times 10^{N}$ ,

where $1 \le a < 10$ and is an integer.

Each factor can be rewritten in scientific notation as follows:

$5,000,000 = 5 \times 1,000,000 = 5 \times 10^{6}$

$120,000,000 = 1.2 \times 100,000,000 = 1.2 \times 10^{8}$

Now, substitute:

$5,000,000 \times 120,000,000$

$= 5 \times 10^{6} \times 1.2 \times 10^{8}$

$=( 5\times 1.2) \times (10^{6} \times 10^{8})$

$= 6 \times 10^{6} \times 10^{8}$

Apply the Product of Powers Property:

$= 6 \times 10^{6+8}$

$= 6 \times 10^{14}$

This is in scientific notation and is the correct choice.

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