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Math

Question Multiply 23.09623.096 and 90.30090.300. Express the result in scientific notation with correct significant figures.

Studdy Solution

STEP 1

Assumptions
1. The numbers given are 23.096 and 90.300.
2. The operation to perform is multiplication.
3. The result should be expressed in scientific notation.
4. The number of significant figures in the final answer should match the number of significant figures in the least precise number used in the calculation.

STEP 2

Identify the number of significant figures in each number.
- 23.096 has 5 significant figures. - 90.300 has 5 significant figures.
Since both numbers have the same number of significant figures, the result should also be rounded to 5 significant figures.

STEP 3

Perform the multiplication operation.
23.096×90.30023.096 \times 90.300

STEP 4

Use a calculator or perform the multiplication manually to find the product.
23.096×90.300=2085.376823.096 \times 90.300 = 2085.3768

STEP 5

Round the result to 5 significant figures, since that is the number of significant figures in the least precise number.
2085.3768≈2085.42085.3768 \approx 2085.4

STEP 6

Express the rounded result in scientific notation.
To convert to scientific notation, we need to express the number as a product of a number between 1 and 10 and a power of 10.
2085.4=2.0854×1032085.4 = 2.0854 \times 10^3

STEP 7

Write the final answer in scientific notation with the correct number of significant figures.
23.096×90.300=2.0854×10323.096 \times 90.300 = 2.0854 \times 10^3

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