QuestionFind the sum of $2.35 \times 10^{19}$ and $3.157 \times 10^{17}$ . Choices: $2.38157 \times 10^{19}$ , $3.1805 \times 10^{19}$ , $2.38157 \times 10^{36}$ , $3.1805 \times 10^{36}$ .

Studdy Solution

STEP 1

Assumptions1. The numbers are in scientific notation, which is a way of expressing very large or very small numbers. . The base of the exponent is10.
3. We are asked to find the sum of the two numbers.

STEP 2

To add two numbers in scientific notation, they must have the same exponent. In this case, the exponents are different (19 and17), so we need to adjust one of the numbers to have the same exponent. We can do this by moving the decimal point in the number with the smaller exponent.

STEP 3

Let's adjust $3.157 \times10^{17}$ to have an exponent of19. To do this, we need to move the decimal point two places to the left, which increases the exponent by2.
$3.157 \times10^{17} =0.03157 \times10^{19}$

STEP 4

Now that both numbers have the same exponent, we can add them together.
$2.35 \times10^{19} +0.03157 \times10^{19}$

STEP 5

We can factor out the common factor of $10^{19}$ , then add the decimal numbers.
$10^{19} \times (2.35 +0.03157)$

STEP 6

Calculate the sum of the decimal numbers.
$10^{19} \times2.38157$ So, the sum of $2.35 \times10^{19}$ and $3.157 \times10^{17}$ is $2.38157 \times10^{19}$ .

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QuestionFind the sum of $2.35 \times 10^{19}$ and $3.157 \times 10^{17}$ . Choices: $2.38157 \times 10^{19}$ , $3.1805 \times 10^{19}$ , $2.38157 \times 10^{36}$ , $3.1805 \times 10^{36}$ .

Studdy Solution

STEP 1

Assumptions1. The numbers are in scientific notation, which is a way of expressing very large or very small numbers. . The base of the exponent is10.
3. We are asked to find the sum of the two numbers.

STEP 2

To add two numbers in scientific notation, they must have the same exponent. In this case, the exponents are different (19 and17), so we need to adjust one of the numbers to have the same exponent. We can do this by moving the decimal point in the number with the smaller exponent.

STEP 3

Let's adjust $3.157 \times10^{17}$ to have an exponent of19. To do this, we need to move the decimal point two places to the left, which increases the exponent by2.
$3.157 \times10^{17} =0.03157 \times10^{19}$

STEP 4

Now that both numbers have the same exponent, we can add them together.
$2.35 \times10^{19} +0.03157 \times10^{19}$

STEP 5

We can factor out the common factor of $10^{19}$ , then add the decimal numbers.
$10^{19} \times (2.35 +0.03157)$

STEP 6

Calculate the sum of the decimal numbers.
$10^{19} \times2.38157$ So, the sum of $2.35 \times10^{19}$ and $3.157 \times10^{17}$ is $2.38157 \times10^{19}$ .

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Studdy Solution

STEP 1

Assumptions1. The numbers are in scientific notation, which is a way of expressing very large or very small numbers. . The base of the exponent is10.3. We are asked to find the sum of the two numbers.

STEP 2

To add two numbers in scientific notation, they must have the same exponent. In this case, the exponents are different (19 and17), so we need to adjust one of the numbers to have the same exponent. We can do this by moving the decimal point in the number with the smaller exponent.

STEP 3

Let's adjust 3.157×10173.157 \times10^{17}3.157×1017 to have an exponent of19. To do this, we need to move the decimal point two places to the left, which increases the exponent by2.3.157×1017=0.03157×10193.157 \times10^{17} =0.03157 \times10^{19}3.157×1017=0.03157×1019

STEP 4

Now that both numbers have the same exponent, we can add them together.2.35×1019+0.03157×10192.35 \times10^{19} +0.03157 \times10^{19}2.35×1019+0.03157×1019

STEP 5

We can factor out the common factor of 101910^{19}1019, then add the decimal numbers.1019×(2.35+0.03157)10^{19} \times (2.35 +0.03157)1019×(2.35+0.03157)

STEP 6

Calculate the sum of the decimal numbers.1019×2.3815710^{19} \times2.381571019×2.38157So, the sum of 2.35×10192.35 \times10^{19}2.35×1019 and 3.157×10173.157 \times10^{17}3.157×1017 is 2.38157×10192.38157 \times10^{19}2.38157×1019.

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Studdy solves anything!

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions1. The numbers are in scientific notation, which is a way of expressing very large or very small numbers. . The base of the exponent is10.
3. We are asked to find the sum of the two numbers.

Let's adjust $3.157 \times10^{17}$ to have an exponent of19. To do this, we need to move the decimal point two places to the left, which increases the exponent by2.
$3.157 \times10^{17} =0.03157 \times10^{19}$

Now that both numbers have the same exponent, we can add them together.
$2.35 \times10^{19} +0.03157 \times10^{19}$

We can factor out the common factor of $10^{19}$ , then add the decimal numbers.
$10^{19} \times (2.35 +0.03157)$

Calculate the sum of the decimal numbers.
$10^{19} \times2.38157$ So, the sum of $2.35 \times10^{19}$ and $3.157 \times10^{17}$ is $2.38157 \times10^{19}$ .