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Significant Digits and Scientific Notation

Learn how to identify, round, and convert numbers using significant digits and scientific notation in this comprehensive guide for science enthusiasts.

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Significant Digits and Scientific Notation

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  1. Significant Digits and Scientific Notation

  2. Significant Digits • Using significant digits is a way of rounding in science. • It uses the digits that are statistically of value or significant.

  3. Identifying Significant Digits • Non-zero numbers are always significant • Example: 22 has 2 significant digits, 22.3 has 3 significant digits • Zeros between two significant digits are also significant. • Example: 101.12 has 5 significant digits because the 0 is between the 1s. • All zeros appearing to the right of an understood decimal point and non-zero digits are significant • Example: 12.2300 has six significant digits. 0.0012300 still has six significant digits because the 0s before the 1 are not significant.

  4. Identifying Significant Digits • All zeros appearing in a number without a decimal point and to the right of the last non-zero digit are not significant unless indicated by a decimal. • Example: '1300' has two significant figures: 1 and 3. • The zeros are not considered significant because they don't have a decimal. • However, 1300.0 has five significant figures.

  5. Examples of Rounding to Significant Digits • Rounding to 2 significant digits • 12,300 becomes • 12,000 • 0.00123 becomes • 0.0012 • 0.1 becomes • 0.10 (the trailing zero indicates that we are rounding to 2 significant figures). • 0.02084 becomes • 0.021

  6. What is Scientific Notation? • Notation for writing numbers used by scientists to record numbers that are very large or very small. • Example: The mass of the Earth is 5,979,000,000,000,000,000,000,000,000 kilograms.This can be recorded as 5.979 x 1027 kg if using scientific notation.

  7. Common Method of Converting from Standard Notation to Scientific Notation • The common practice is to move the decimal over to the point where you have the right number of significant digits. • If the number is really small, the decimal is moved to the right. • If the number is really large, the decimal is moved to the left.

  8. Example large number • Write 4,567,000 using scientific notation. • Move the decimal to the left. • 4.567000 • Count how many places you moved the decimal. • 6 • Now put it in scientific notation • 4.567 x 106

  9. Example Small Number • Write 0.00000005436 using scientific notation. • Move the decimal to the right • 5.436 • Count how many places you moved the decimal • 8 • Since you moved to the right it has to be negative • -8 • Put it in scientific notation • 5.436 x 10-8

  10. Try on Your Own: • 7,943,000 • Answer: • 7.943 x 106 • 0.0000004302 • Answer: • 4.302 x 10-7

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