Express the number 0.000216 in scientific notation (2.16 x 10^-4). Express 166,000 in exponential (scientific) notation (1.66 x 10^5). Express the number 8.64 x 10^-3 in common decimal form (0.00864). Express the number 1.16 x 10^4 in common decimal form (11600). How many significant figures are there in the number 0.045607007 (7)
The Correct Answer and Explanation is:
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Correct Answers:
- Scientific notation of 0.000216:
✅ 2.16 × 10⁻⁴ - Scientific notation of 166,000:
✅ 1.66 × 10⁵ - Decimal form of 8.64 × 10⁻³:
✅ 0.00864 - Decimal form of 1.16 × 10⁴:
✅ 11,600 - Significant figures in 0.045607007:
✅ 7 significant figures
Explanation:
Scientific notation is a way of expressing very large or very small numbers in a compact form, especially useful in science and engineering. It’s written in the form:
a×10na \times 10^na×10n
where aaa is a number between 1 and 10, and nnn is an integer.
Let’s break down each case:
- 0.000216 → 2.16 × 10⁻⁴:
Move the decimal point 4 places to the right to get 2.16. Since we made the number bigger, the exponent is negative. - 166,000 → 1.66 × 10⁵:
Move the decimal point 5 places to the left. We reduce the number’s size, so the exponent is positive. - 8.64 × 10⁻³ → 0.00864:
Move the decimal 3 places to the left, as the exponent is negative. This gives the correct decimal. - 1.16 × 10⁴ → 11,600:
Move the decimal 4 places to the right due to the positive exponent.
Now, about significant figures:
Significant figures are the digits in a number that carry meaningful contributions to its measurement accuracy. Rules include:
- All non-zero digits are significant.
- Zeros between non-zero digits are significant.
- Leading zeros (zeros before the first non-zero digit) are not significant.
- Trailing zeros in a decimal are significant.
For the number 0.045607007:
- Ignore the leading zeros (0.0).
- All the digits after that (4, 5, 6, 0, 7, 0, 0, 7) are significant.
- That gives us 7 significant figures.
Knowing how to work with scientific notation and significant figures is essential for precision in scientific communication and calculations.
