Mathematical ToolkitMathematical Toolkit

ReviewReview

Significant DigitsSignificant Digits

Nonzero digits are always significant.Nonzero digits are always significant. All final zeros to the right of the decimal All final zeros to the right of the decimal

point are significant.point are significant. Zeros between two other significant digits Zeros between two other significant digits

are always significant.are always significant. Zeros used solely for spacing the decimal Zeros used solely for spacing the decimal

point are not significant.point are not significant.

Scientific NotationScientific Notation

Expressing decimal places as a power of 10Expressing decimal places as a power of 10

M x 10M x 10nn

Where 1 Where 1 ≤ M < 10≤ M < 10– One digit to the left of the decimal pointOne digit to the left of the decimal point

Scientific Notation with CalculatorsScientific Notation with Calculators

M EnM En

Math Operations with Sig. DigitsMath Operations with Sig. Digits

When Adding and SubtractingWhen Adding and Subtracting:: If the n values are the same, add the M values and If the n values are the same, add the M values and

keep the n value the same.keep the n value the same. If the n values are not the same, move the decimal If the n values are not the same, move the decimal

until they are the same and repeat the above step.until they are the same and repeat the above step. When the magnitude of one number is quite small When the magnitude of one number is quite small

compared to the other, its effect on the larger compared to the other, its effect on the larger number is insignificant. The smaller number can number is insignificant. The smaller number can be treated as zero.be treated as zero.

Math Operations with Sig. DigitsMath Operations with Sig. Digits

When MultiplyingWhen Multiplying:: Multiply the M values.Multiply the M values. Add the exponents (n)Add the exponents (n)

When DividingWhen Dividing:: Divide the M values.Divide the M values. Subtract the exponent divisor (bottom) from Subtract the exponent divisor (bottom) from

the exponent of the dividend (top). (top – the exponent of the dividend (top). (top – bottom)bottom)