Significant Digits and Scientific Notation Significant Digits Using

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Significant Digits and Scientific Notation

Significant Digits and Scientific Notation

Significant Digits • Using significant digits is a way of rounding in science. •

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

Identifying Significant Digits • Non-zero numbers are always significant – Example: 22 has 2

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 1 s. • 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 0 s before the 1 are not significant.

Identifying Significant Digits • All zeros appearing in a number without a decimal point

Identifying Significant Digits • All zeros appearing in a number without a decimal point and to the right of the last nonzero 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.

Examples of Rounding to Significant Digits • Rounding to 2 significant digits – 12,

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

What is Scientific Notation? • Notation for writing numbers used by scientists to record

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 kilograms. This can be recorded as 5. 979 x 1027 kg if using scientific notation.

Common Method of Converting from Standard Notation to Scientific Notation • The common practice

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.

Example large number • Write 4, 567, 000 using scientific notation. • Move the

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

Example Small Number • Write 0. 00000005436 using scientific notation. • Move the decimal

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

Try on Your Own: • 7, 943, 000 – Answer: • 7. 943 x

Try on Your Own: • 7, 943, 000 – Answer: • 7. 943 x 106 • 0. 0000004302 – Answer: • 4. 302 x 10 -7