A Few Worked Problems

Here are a few worked problems that involve various uses of scientific notation.

• This problem calls for you to convert a number in scientific notation to an integer value.

  6.3 × 10⁴ = 6.3 × 10,000 = 63,000

  To convert a number from its scientific form to an integer, you begin with the rational form of the number, and then multiply it by a number consisting of 1 and a number of zeros corresponding to the number of the exponent of 10.

• When you deal with values that are a fraction of 1, you can determine how to shift the number by converting the exponential form of 10 into a fraction.

  

  10 raised to the power of 2 is 100, and when you multiply 6.3 by 1/100, you shift the decimal point two digits to the left.

• In this situation, to represent the rational number in scientific notation, you begin by converting the denominator to a power of ten.

  

  You then use a negative exponent to convert the number into scientific notation.

• Here are a couple of examples of converting back and forth. In the first example, you shift the decimal point to the right two places to reflect the exponent of 10. In the lower example, you begin with an integer value. To make it clearer how to convert the number from scientific notation to a rational number, you can convert the integer to a rational number, and then shift the decimal point three digits to the left.

  2.908 × 10² = 290.8

  4 × 10^-3 = 4.0 × 10^-3 =.004

• If you can find ways to reduce the complexity of fractions, then it becomes easier to deal with scientific notation. In this case, you begin with a numerator that requires you to multiply two numbers given in scientific notation.

  

  You multiply 2 by 4 to arrive at 8 in the numerator. When you rewrite the expression so that 8/8 equals 1, then you are in a position to work with only the exponents of 10. To carry out the division, you subtract the negative exponent of the denominator from the positive exponent of the numerator, resulting in 10 to the power of 9.