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Scientific Notation and Significant Figures in General Chemistry

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  • What is scientific notation?

    Scientific notation is a system for expressing very large or very small numbers as a simple number between 1 and 10 multiplied by 10 raised to an exponent.

  • How is a number written in scientific notation?

    A number is written as \(y \times 10^x\), where y is the coefficient (1 to 10) and x is the exponent (positive or negative whole number).

  • What does a positive exponent in scientific notation indicate?

    A positive exponent means the number's magnitude is greater than one.

  • What does a negative exponent in scientific notation indicate?

    A negative exponent means the number's magnitude is less than one.

  • How do you convert scientific notation to standard notation?

    Move the decimal point to the right if the exponent is positive, or to the left if negative, adding zeros as needed to get the proper magnitude.

  • What are significant figures?

    Significant figures are all digits known with certainty plus the first uncertain (estimated) digit in a measurement.

  • Which digits are always significant?

    All nonzero digits and captive zeros (zeros between significant digits) are always significant.

  • Are leading zeros significant?

    No, leading zeros in decimal numbers less than 1 are not significant; they only position the decimal point.

  • When are trailing zeros significant?

    Trailing zeros are significant only if the number contains a decimal point.

  • How many significant figures are in 0.000458?

    Three significant figures: 4, 5, and 8; the leading zeros are not significant.

  • How many significant figures are in 1,500 and 1,500.00?

    1,500 has two significant figures; 1,500.00 has six significant figures because of the decimal point.

  • How do you determine significant figures in addition or subtraction?

    Align decimal points and limit the answer to the rightmost column where all numbers have significant figures.

  • How do you determine significant figures in multiplication or division?

    Limit the answer to the lowest number of significant figures among the numbers used.

  • How does scientific notation help with significant figures?

    It clearly communicates the number of significant figures by including them in the coefficient.

  • How would you write 450 with two significant figures in scientific notation?

    4.5 × 10\(2\)

  • How would you write 450.0 with four significant figures in scientific notation?

    4.500 × 10\(2\)

  • Example: How many significant figures in 38.65 and 105.93?

    38.65 has 4 significant figures; 105.93 has 5 significant figures.

  • How to reduce the product 38.65 × 105.93 to 4 significant figures?

    Calculate the product and round the result to 4 significant figures, e.g., 4,094.1945 rounded to 4,094.