What is $56,490,000$ written in scientific notation?
A. $56.49 \times 10^6$
B. $5.649 \times 10^{-7}$
C. $5.649 \times 10^8$
D. $5.649 \times 10^7$
Answer (2)
Convert the number to the form a × 1 0 b , where 1 ≤ a < 10 .
Move the decimal point in 56 , 490 , 000 to the left until you have 5.649 .
Count the number of places you moved the decimal point, which is 7, so b = 7 .
Write the number in scientific notation: 5.649 × 1 0 7 .
Explanation
Understanding Scientific Notation We are asked to express the number 56 , 490 , 000 in scientific notation. Scientific notation is a way of writing numbers as a product of a number between 1 and 10 (including 1 but excluding 10) and a power of 10. This makes it easier to work with very large or very small numbers.
Moving the Decimal Point To convert 56 , 490 , 000 to scientific notation, we need to move the decimal point until we have a number between 1 and 10. The decimal point is currently at the end of the number, so we have 56490000. We move the decimal point 7 places to the left to get 5.6490000 , which is 5.649 .
Determining the Exponent Since we moved the decimal point 7 places to the left, we multiply 5.649 by 1 0 7 to get the original number back. Therefore, 56 , 490 , 000 = 5.649 × 1 0 7 .
Final Answer Thus, 56 , 490 , 000 written in scientific notation is 5.649 × 1 0 7 .
Examples
Scientific notation is extremely useful in fields like astronomy and physics, where dealing with very large and very small numbers is common. For example, the distance to the nearest star, Proxima Centauri, is approximately 40,208,000,000,000 kilometers. Writing this in scientific notation as 4.0208 × 1 0 13 km makes it much easier to handle and compare with other astronomical distances. Similarly, the mass of an electron is about 0.00000000000000000000000000000091093837 kg, which can be written in scientific notation as 9.1093837 × 1 0 − 31 kg.
The scientific notation for 56 , 490 , 000 is 5.649 × 1 0 7 . This is achieved by moving the decimal point 7 places to the left. The correct option is D.
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