Express the following in the scientific notation : (a) 0.0048 (b) 234,000 (c) 8008 (d) 500.0 (e) 6.0012
The correct answer and explanation is:
Correct Answers in Scientific Notation:
(a) 0.0048 = 4.8 × 10⁻³
(b) 234,000 = 2.34 × 10⁵
(c) 8008 = 8.008 × 10³
(d) 500.0 = 5.000 × 10²
(e) 6.0012 = 6.0012 × 10⁰
Explanation:
Scientific notation is a method of expressing numbers that are too large or too small in a compact and manageable form. It is written in the form:
a × 10ⁿ,
where a is a number greater than or equal to 1 but less than 10, and n is an integer.
To convert a number into scientific notation:
- Identify the decimal point’s new position so that only one non-zero digit remains to its left.
- Count the number of places the decimal moves. This becomes the exponent n of 10.
- If the original number is less than 1, the exponent n is negative. If the number is greater than or equal to 10, the exponent n is positive.
Example (a):
0.0048 becomes 4.8 after moving the decimal point 3 places to the right. This gives 4.8 × 10⁻³.
Example (b):
234,000 becomes 2.34 after moving the decimal point 5 places to the left. So, 2.34 × 10⁵.
Example (c):
8008 becomes 8.008 after moving the decimal point 3 places to the left. Hence, 8.008 × 10³.
Example (d):
500.0 becomes 5.000 after moving the decimal 2 places left. So, 5.000 × 10². The zeroes after the decimal are significant because they indicate measurement precision.
Example (e):
6.0012 already falls in the correct range for the coefficient. Since no shift of the decimal is needed, the exponent is 0. Therefore, it is 6.0012 × 10⁰.
Scientific notation helps simplify calculations, especially in science and engineering, by making it easier to handle extremely large or small values.