Express each of the following numbers in exponential notation: (a) 2,900,000 (c) 0.00840 (b) 0.587 (d) 0.0000055
The Correct Answer and Explanation is :
To express numbers in exponential notation (also known as scientific notation), we write them as a product of a number between 1 and 10 and a power of 10. The format is:
[
a \times 10^n
]
Where:
- (a) is a number between 1 and 10.
- (n) is the exponent, which represents how many places the decimal point moves.
Now, let’s convert each of the given numbers into exponential notation:
(a) 2,900,000
To convert 2,900,000 into exponential notation:
- We move the decimal point 6 places to the left to get the number 2.9, which is between 1 and 10.
- The exponent will be 6 because we moved the decimal 6 places.
Thus, the number in exponential notation is:
[
2.9 \times 10^6
]
(b) 0.587
To convert 0.587 into exponential notation:
- We move the decimal point 3 places to the right to get the number 5.87, which is between 1 and 10.
- The exponent will be -3 because we moved the decimal point to the right.
Thus, the number in exponential notation is:
[
5.87 \times 10^{-1}
]
(c) 0.00840
To convert 0.00840 into exponential notation:
- We move the decimal point 3 places to the right to get 8.40, which is between 1 and 10.
- The exponent will be -3 because the decimal point moves to the right.
Thus, the number in exponential notation is:
[
8.40 \times 10^{-3}
]
(d) 0.0000055
To convert 0.0000055 into exponential notation:
- We move the decimal point 6 places to the right to get 5.5, which is between 1 and 10.
- The exponent will be -6 because we moved the decimal point to the right.
Thus, the number in exponential notation is:
[
5.5 \times 10^{-6}
]
Explanation:
Exponential notation is used to simplify very large or very small numbers. It provides a more concise way to express numbers by adjusting the decimal point and using exponents. The exponent indicates how many places the decimal has moved and whether the number is large (positive exponent) or small (negative exponent). This notation is especially useful in fields like science and engineering, where working with such numbers is common.