Solve problems using scientific notation - HiSET

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Multiply, and express the product in scientific notation:

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

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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.

Simplify the following expression using scientific notation.

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You can solve this problem in several ways. One way is to convert each number out of scientific notation and write it out fully, then find the sum of the two values and convert the answer back into scientific notation.

Another, potentially faster, way to solve this problem is to convert one answer into the same scientific-notational terms as the other and then sum them.

Multiply:

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

Express the product in scientific notation.

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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.

Simplify the following expression using scientific notation.

Tap to see back →

You can solve this problem in several ways. One way is to convert each number out of scientific notation and write it out fully, then find the sum of the two values and convert the answer back into scientific notation.

Another, potentially faster, way to solve this problem is to convert one answer into the same scientific-notational terms as the other and then sum them.

Multiply, and express the product in scientific notation:

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

Tap to see back →

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.

Multiply:

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

Express the product in scientific notation.

Tap to see back →

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.

Simplify the following expression using scientific notation.

Tap to see back →

You can solve this problem in several ways. One way is to convert each number out of scientific notation and write it out fully, then find the sum of the two values and convert the answer back into scientific notation.

Another, potentially faster, way to solve this problem is to convert one answer into the same scientific-notational terms as the other and then sum them.

Multiply, and express the product in scientific notation:

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

Tap to see back →

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.

Multiply:

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

Express the product in scientific notation.

Tap to see back →

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.

Simplify the following expression using scientific notation.

Tap to see back →

You can solve this problem in several ways. One way is to convert each number out of scientific notation and write it out fully, then find the sum of the two values and convert the answer back into scientific notation.

Another, potentially faster, way to solve this problem is to convert one answer into the same scientific-notational terms as the other and then sum them.

Multiply, and express the product in scientific notation:

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

Tap to see back →

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.

Multiply:

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

Express the product in scientific notation.

Tap to see back →

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.