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Math  /  Numbers & Operations

QuestionQuestion
What is the product of 3500 and 5.6×1045.6 \times 10^{4} expressed in scientific notation?

Studdy Solution

STEP 1

1. We need to find the product of 3500 3500 and 5.6×104 5.6 \times 10^{4} .
2. The result should be expressed in scientific notation.

STEP 2

1. Convert 3500 to scientific notation.
2. Multiply the numbers in scientific notation.
3. Express the result in proper scientific notation.

STEP 3

Convert 3500 3500 to scientific notation.
3500=3.5×103 3500 = 3.5 \times 10^{3}

STEP 4

Multiply the numbers in scientific notation.
(3.5×103)×(5.6×104) (3.5 \times 10^{3}) \times (5.6 \times 10^{4})

STEP 5

Multiply the coefficients 3.5 3.5 and 5.6 5.6 .
3.5×5.6=19.6 3.5 \times 5.6 = 19.6

STEP 6

Add the exponents of 103 10^{3} and 104 10^{4} .
103×104=107 10^{3} \times 10^{4} = 10^{7}

STEP 7

Combine the results to express the product in scientific notation.
19.6×107 19.6 \times 10^{7}

STEP 8

Adjust 19.6×107 19.6 \times 10^{7} to proper scientific notation.
19.6=1.96×101 19.6 = 1.96 \times 10^{1} 1.96×101×107=1.96×108 1.96 \times 10^{1} \times 10^{7} = 1.96 \times 10^{8}
The product of 3500 3500 and 5.6×104 5.6 \times 10^{4} expressed in scientific notation is:
1.96×108\boxed{1.96 \times 10^{8}}

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