Convert the following numbers into scientific notation: 27 000 000 = 0.000 007 12 = 821 = 0.000 101 = 81 250 000 000 = 0.000 000 002 05 = (a) (b) (f) 2. Change the following numbers into normal notation: (a) 5.80 x 10^6 (b) 6.32 x 10^5 (c) 8.56 x 10^4 (d) 2.52 x 10^3 (e) 2.30 x 10^10 (f) 6.10 x 10^-11 3. Rewrite 2800 in scientific notation having 2 significant figures.
The Correct Answer and Explanation is:
1. Convert the following numbers into scientific notation:
- 27 000 000 = 2.7 × 10⁷
- 0.000 007 12 = 7.12 × 10⁻⁶
- 821 = 8.21 × 10²
- 0.000 101 = 1.01 × 10⁻⁴
- 81 250 000 000 = 8.125 × 10¹⁰
- 0.000 000 002 05 = 2.05 × 10⁻⁹
2. Change the following numbers into normal (standard) notation:
(a) 5.80 × 10⁶ = 5,800,000
(b) 6.32 × 10⁵ = 632,000
(c) 8.56 × 10⁴ = 85,600
(d) 2.52 × 10³ = 2,520
(e) 2.30 × 10¹⁰ = 23,000,000,000
(f) 6.10 × 10⁻¹¹ = 0.0000000000610
3. Rewrite 2800 in scientific notation having 2 significant figures:
Answer: 2.8 × 1
Scientific notation is a method of expressing very large or very small numbers in a more compact and manageable form. It is especially useful in science, engineering, and mathematics where such numbers are common. The general format of scientific notation is:
a × 10ⁿ,
where 1 ≤ a < 10 and n is an integer.
To convert a number into scientific notation, you move the decimal point to create a number between 1 and 10, then multiply by a power of 10 that reflects how many places the decimal point was moved. If you move the decimal to the left, the exponent is positive. If you move it to the right, the exponent is negative.
For example, 27,000,000 becomes 2.7 × 10⁷ because the decimal point is moved 7 places to the left. Similarly, 0.00000712 becomes 7.12 × 10⁻⁶ since the decimal moves 6 places to the right.
When converting from scientific to standard notation, you simply move the decimal point as indicated by the exponent. A positive exponent means move it to the right; a negative exponent means to the left.
Regarding significant figures, these are the digits in a number that carry meaning. When asked to write 2800 in scientific notation with 2 significant figures, we keep the two most meaningful digits (“2” and “8”) and express it as 2.8 × 10³. Writing it as 2.80 × 10³ would imply three significant figures, which is not what’s asked.
Using scientific notation ensures clarity and precision in communicating data, especially in contexts where scale matters greatly
