In scientific notation, the number $185,000,000$ is
A. $185 \times 10^6$
B. $1.85 \times 10^8$
C. $1.85 \times 10^{-8}$
D. $185 \times 10^{-8}$
E. $1.85 \times 10^6$
Answer (2)
Express the number in the form a × 1 0 b , where 1 ≤ a < 10 .
Move the decimal point in 185 , 000 , 000 to the left until there is only one non-zero digit to the left of the decimal point, resulting in 1.85 .
Count the number of places the decimal point was moved (8 places), which gives the exponent b = 8 .
Write the number in scientific notation: 1.85 × 1 0 8 .
Explanation
Understanding Scientific Notation We are asked to express the number 185 , 000 , 000 in scientific notation. Scientific notation is a way of writing numbers as a product of a number between 1 and 10 (including 1) and a power of 10.
Moving the Decimal Point To convert 185 , 000 , 000 to scientific notation, we need to move the decimal point until we have a number between 1 and 10. In this case, we move the decimal point 8 places to the left to get 1.85 .
Determining the Exponent Since we moved the decimal point 8 places to the left, we multiply 1.85 by 1 0 8 to get the original number. Therefore, 185 , 000 , 000 = 1.85 × 1 0 8 .
Final Answer The number 185 , 000 , 000 in scientific notation is 1.85 × 1 0 8 .
Examples
Scientific notation is extremely useful in fields like astronomy and physics, where dealing with very large or very small numbers is common. For instance, the distance to a star might be 1,500,000,000,000 meters, which is more easily written as 1.5 × 1 0 12 meters. Similarly, the size of a virus might be 0.000000025 meters, which is more conveniently expressed as 2.5 × 1 0 − 8 meters. Using scientific notation simplifies calculations and makes these numbers more manageable.
The number 185 , 000 , 000 can be expressed in scientific notation as 1.85 × 1 0 8 by moving the decimal point 8 places to the left. This not only simplifies the representation of large numbers but also makes calculations easier. The correct answer is option B: 1.85 × 1 0 8 .
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