Solved on Nov 17, 2023

Add $2.3 \cdot 10^{8}$ and $4.7 \cdot 10^{7}$ and express the result in scientific notation.

STEP 1

Assumptions1. We are given two numbers in scientific notation $.3 \cdot10^{8}$ and $4.7 \cdot10^{7}$ . We are asked to add these two numbers together3. The final answer should also be expressed in scientific notation

STEP 2

To add these two numbers, we first need to express them with the same exponent. We can do this by converting $4.7 \cdot10^{7}$ to the form $x \cdot10^{8}$ .

STEP 3

To convert $.7 \cdot10^{7}$ to the form $x \cdot10^{8}$ , we divide $.7$ by $10$ and increase the exponent by $1$ .
$.7 \cdot10^{7} = \frac{.7}{10} \cdot10^{8}$

STEP 4

Calculate the new value of $4.7 \cdot10^{7}$ .
$4.7 \cdot10^{7} =0.47 \cdot10^{8}$

STEP 5

Now that both numbers are expressed with the same exponent, we can add them together.
$2.3 \cdot10^{8} +0.47 \cdot10^{8} = (2.3 +0.47) \cdot10^{8}$

STEP 6

Calculate the sum.
$(2.3 +0.47) \cdot10^{8} =2.77 \cdot10^{8}$ The sum of $2.3 \cdot10^{8}$ and $4. \cdot10^{}$ is $2.77 \cdot10^{8}$ .

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Add $2.3 \cdot 10^{8}$ and $4.7 \cdot 10^{7}$ and express the result in scientific notation.

STEP 1

Assumptions1. We are given two numbers in scientific notation $.3 \cdot10^{8}$ and $4.7 \cdot10^{7}$ . We are asked to add these two numbers together3. The final answer should also be expressed in scientific notation

STEP 2

To add these two numbers, we first need to express them with the same exponent. We can do this by converting $4.7 \cdot10^{7}$ to the form $x \cdot10^{8}$ .

STEP 3

To convert $.7 \cdot10^{7}$ to the form $x \cdot10^{8}$ , we divide $.7$ by $10$ and increase the exponent by $1$ .
$.7 \cdot10^{7} = \frac{.7}{10} \cdot10^{8}$

STEP 4

Calculate the new value of $4.7 \cdot10^{7}$ .
$4.7 \cdot10^{7} =0.47 \cdot10^{8}$

STEP 5

Now that both numbers are expressed with the same exponent, we can add them together.
$2.3 \cdot10^{8} +0.47 \cdot10^{8} = (2.3 +0.47) \cdot10^{8}$

STEP 6

Calculate the sum.
$(2.3 +0.47) \cdot10^{8} =2.77 \cdot10^{8}$ The sum of $2.3 \cdot10^{8}$ and $4. \cdot10^{}$ is $2.77 \cdot10^{8}$ .

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Add 2.3⋅1082.3 \cdot 10^{8}2.3⋅108 and 4.7⋅1074.7 \cdot 10^{7}4.7⋅107 and express the result in scientific notation.

STEP 1

Assumptions1. We are given two numbers in scientific notation .3⋅108.3 \cdot10^{8}.3⋅108 and 4.7⋅1074.7 \cdot10^{7}4.7⋅107 . We are asked to add these two numbers together3. The final answer should also be expressed in scientific notation

STEP 2

To add these two numbers, we first need to express them with the same exponent. We can do this by converting 4.7⋅1074.7 \cdot10^{7}4.7⋅107 to the form x⋅108x \cdot10^{8}x⋅108.

STEP 3

To convert .7⋅107.7 \cdot10^{7}.7⋅107 to the form x⋅108x \cdot10^{8}x⋅108, we divide .7.7.7 by 101010 and increase the exponent by 111..7⋅107=.710⋅108.7 \cdot10^{7} = \frac{.7}{10} \cdot10^{8}.7⋅107=10.7​⋅108

STEP 4

Calculate the new value of 4.7⋅1074.7 \cdot10^{7}4.7⋅107.4.7⋅107=0.47⋅1084.7 \cdot10^{7} =0.47 \cdot10^{8}4.7⋅107=0.47⋅108

STEP 5

Now that both numbers are expressed with the same exponent, we can add them together.2.3⋅108+0.47⋅108=(2.3+0.47)⋅1082.3 \cdot10^{8} +0.47 \cdot10^{8} = (2.3 +0.47) \cdot10^{8}2.3⋅108+0.47⋅108=(2.3+0.47)⋅108

STEP 6

Calculate the sum.(2.3+0.47)⋅108=2.77⋅108(2.3 +0.47) \cdot10^{8} =2.77 \cdot10^{8}(2.3+0.47)⋅108=2.77⋅108The sum of 2.3⋅1082.3 \cdot10^{8}2.3⋅108 and 4.⋅104. \cdot10^{}4.⋅10 is 2.77⋅1082.77 \cdot10^{8}2.77⋅108.

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Add $2.3 \cdot 10^{8}$ and $4.7 \cdot 10^{7}$ and express the result in scientific notation.

Assumptions1. We are given two numbers in scientific notation $.3 \cdot10^{8}$ and $4.7 \cdot10^{7}$ . We are asked to add these two numbers together3. The final answer should also be expressed in scientific notation

To add these two numbers, we first need to express them with the same exponent. We can do this by converting $4.7 \cdot10^{7}$ to the form $x \cdot10^{8}$ .

To convert $.7 \cdot10^{7}$ to the form $x \cdot10^{8}$ , we divide $.7$ by $10$ and increase the exponent by $1$ .
$.7 \cdot10^{7} = \frac{.7}{10} \cdot10^{8}$

Calculate the new value of $4.7 \cdot10^{7}$ .
$4.7 \cdot10^{7} =0.47 \cdot10^{8}$

Now that both numbers are expressed with the same exponent, we can add them together.
$2.3 \cdot10^{8} +0.47 \cdot10^{8} = (2.3 +0.47) \cdot10^{8}$

Calculate the sum.
$(2.3 +0.47) \cdot10^{8} =2.77 \cdot10^{8}$ The sum of $2.3 \cdot10^{8}$ and $4. \cdot10^{}$ is $2.77 \cdot10^{8}$ .