Solved on Jan 16, 2024

Determine the product of $8.9 \times 10^{19}$ and $1.2 \times 10^{2}$ using a calculator.

STEP 1

Assumptions
1. The notation $E$ represents the exponent in scientific notation, where $a E b$ means $a \times 10^b$ .
2. We are using a calculator to perform the multiplication.

STEP 2

First, we need to understand the scientific notation. The expression $8.9 E 19$ means $8.9 \times 10^{19}$ , and $1.2 E 2$ means $1.2 \times 10^2$ .

STEP 3

Now, we will multiply the two numbers in scientific notation.
$8.9 \times 10^{19} \cdot 1.2 \times 10^2$

STEP 4

We can separate the multiplication into two parts: the multiplication of the decimal numbers and the multiplication of the powers of 10.
$(8.9 \cdot 1.2) \times (10^{19} \cdot 10^2)$

STEP 5

First, multiply the decimal numbers using a calculator.
$8.9 \cdot 1.2 = 10.68$

STEP 6

Next, add the exponents when multiplying the powers of 10, according to the rule $10^a \cdot 10^b = 10^{a+b}$ .
$10^{19} \cdot 10^2 = 10^{19+2} = 10^{21}$

STEP 7

Combine the results of the decimal multiplication and the powers of 10 multiplication.
$10.68 \times 10^{21}$

STEP 8

The result in scientific notation is:
$1.068 \times 10^1 \times 10^{21}$

STEP 9

Now, add the exponents of the powers of 10.
$1.068 \times 10^{1+21} = 1.068 \times 10^{22}$

STEP 10

Finally, we write the result in scientific notation.
$8.9 E 19 \cdot 1.2 E 2 = 1.068 \times 10^{22}$
The result of $8.9 E 19 \cdot 1.2 E 2$ using a calculator is $1.068 \times 10^{22}$ .

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Determine the product of $8.9 \times 10^{19}$ and $1.2 \times 10^{2}$ using a calculator.

STEP 1

Assumptions
1. The notation $E$ represents the exponent in scientific notation, where $a E b$ means $a \times 10^b$ .
2. We are using a calculator to perform the multiplication.

STEP 2

First, we need to understand the scientific notation. The expression $8.9 E 19$ means $8.9 \times 10^{19}$ , and $1.2 E 2$ means $1.2 \times 10^2$ .

STEP 3

Now, we will multiply the two numbers in scientific notation.
$8.9 \times 10^{19} \cdot 1.2 \times 10^2$

STEP 4

We can separate the multiplication into two parts: the multiplication of the decimal numbers and the multiplication of the powers of 10.
$(8.9 \cdot 1.2) \times (10^{19} \cdot 10^2)$

STEP 5

First, multiply the decimal numbers using a calculator.
$8.9 \cdot 1.2 = 10.68$

STEP 6

Next, add the exponents when multiplying the powers of 10, according to the rule $10^a \cdot 10^b = 10^{a+b}$ .
$10^{19} \cdot 10^2 = 10^{19+2} = 10^{21}$

STEP 7

Combine the results of the decimal multiplication and the powers of 10 multiplication.
$10.68 \times 10^{21}$

STEP 8

The result in scientific notation is:
$1.068 \times 10^1 \times 10^{21}$

STEP 9

Now, add the exponents of the powers of 10.
$1.068 \times 10^{1+21} = 1.068 \times 10^{22}$

STEP 10

Finally, we write the result in scientific notation.
$8.9 E 19 \cdot 1.2 E 2 = 1.068 \times 10^{22}$
The result of $8.9 E 19 \cdot 1.2 E 2$ using a calculator is $1.068 \times 10^{22}$ .

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Determine the product of 8.9×10198.9 \times 10^{19}8.9×1019 and 1.2×1021.2 \times 10^{2}1.2×102 using a calculator.

STEP 1

Assumptions1. The notation EEE represents the exponent in scientific notation, where aEba E baEb means a×10ba \times 10^ba×10b.2. We are using a calculator to perform the multiplication.

STEP 2

First, we need to understand the scientific notation. The expression 8.9E198.9 E 198.9E19 means 8.9×10198.9 \times 10^{19}8.9×1019, and 1.2E21.2 E 21.2E2 means 1.2×1021.2 \times 10^21.2×102.

STEP 3

Now, we will multiply the two numbers in scientific notation.8.9×1019⋅1.2×1028.9 \times 10^{19} \cdot 1.2 \times 10^28.9×1019⋅1.2×102

STEP 4

We can separate the multiplication into two parts: the multiplication of the decimal numbers and the multiplication of the powers of 10.(8.9⋅1.2)×(1019⋅102)(8.9 \cdot 1.2) \times (10^{19} \cdot 10^2)(8.9⋅1.2)×(1019⋅102)

STEP 5

First, multiply the decimal numbers using a calculator.8.9⋅1.2=10.688.9 \cdot 1.2 = 10.688.9⋅1.2=10.68

STEP 6

Next, add the exponents when multiplying the powers of 10, according to the rule 10a⋅10b=10a+b10^a \cdot 10^b = 10^{a+b}10a⋅10b=10a+b.1019⋅102=1019+2=102110^{19} \cdot 10^2 = 10^{19+2} = 10^{21}1019⋅102=1019+2=1021

STEP 7

Combine the results of the decimal multiplication and the powers of 10 multiplication.10.68×102110.68 \times 10^{21}10.68×1021

STEP 8

The result in scientific notation is:1.068×101×10211.068 \times 10^1 \times 10^{21}1.068×101×1021

STEP 9

Now, add the exponents of the powers of 10.1.068×101+21=1.068×10221.068 \times 10^{1+21} = 1.068 \times 10^{22}1.068×101+21=1.068×1022

STEP 10

Finally, we write the result in scientific notation.8.9E19⋅1.2E2=1.068×10228.9 E 19 \cdot 1.2 E 2 = 1.068 \times 10^{22}8.9E19⋅1.2E2=1.068×1022The result of 8.9E19⋅1.2E28.9 E 19 \cdot 1.2 E 28.9E19⋅1.2E2 using a calculator is 1.068×10221.068 \times 10^{22}1.068×1022.

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

Determine the product of $8.9 \times 10^{19}$ and $1.2 \times 10^{2}$ using a calculator.

Assumptions
1. The notation $E$ represents the exponent in scientific notation, where $a E b$ means $a \times 10^b$ .
2. We are using a calculator to perform the multiplication.

First, we need to understand the scientific notation. The expression $8.9 E 19$ means $8.9 \times 10^{19}$ , and $1.2 E 2$ means $1.2 \times 10^2$ .

Now, we will multiply the two numbers in scientific notation.
$8.9 \times 10^{19} \cdot 1.2 \times 10^2$

We can separate the multiplication into two parts: the multiplication of the decimal numbers and the multiplication of the powers of 10.
$(8.9 \cdot 1.2) \times (10^{19} \cdot 10^2)$

First, multiply the decimal numbers using a calculator.
$8.9 \cdot 1.2 = 10.68$

Next, add the exponents when multiplying the powers of 10, according to the rule $10^a \cdot 10^b = 10^{a+b}$ .
$10^{19} \cdot 10^2 = 10^{19+2} = 10^{21}$

Combine the results of the decimal multiplication and the powers of 10 multiplication.
$10.68 \times 10^{21}$

The result in scientific notation is:
$1.068 \times 10^1 \times 10^{21}$

Now, add the exponents of the powers of 10.
$1.068 \times 10^{1+21} = 1.068 \times 10^{22}$

Finally, we write the result in scientific notation.
$8.9 E 19 \cdot 1.2 E 2 = 1.068 \times 10^{22}$
The result of $8.9 E 19 \cdot 1.2 E 2$ using a calculator is $1.068 \times 10^{22}$ .