Using Scientific Measurements

Using Scientific Measurements

Numbers, numbers, numbers...

Accuracy and Precision

• Accuracy refers to the closeness of measurements to the correct or accepted value of the quantity measured

• Precision refers to the closeness of a set of measurements of the same quantity made the same way

Percentage Error

Percentage error tells us by what percentage we are off from the accepted value of a quantity. The value is negative if the measured value is too small. It's positive if the measured value is too large.

Fill in the Blank

A student calculates the density of a substance as $1.40\ \frac{g}{mL}$ . The accepted value of the density is  $1.30\ \frac{g}{mL}$ . What is the percentage error of the student's measurement to the tenth's place?

Rounding Rules:

• If the number is 4 or less, then the current number stays (i.e. Rounding 1.44 to the tenth's place is 1.4)

• If the number is 5 or greater, the number rounds up (i.e. Rounding 9.725 to the hundredth's place makes the number 9.73)

Fill in the Blank

Round 912 to the hundred's place.

Fill in the Blank

Round 21.95 to the tenth's place.

Scientific Notation is a shorthand method of writing incredibly large and incredibly small numbers

Rules for Scientific Notation (Form:  $M\times10^n$ )

• The integer (often represented by M) must be between 1 and 10.

• If the power of 10 (often represented by n) is negative, the number is incredibly small. If it is positive, then it is incredibly large.

The digit to the left of the decimal point must be between 1 and 10 (or, a nonzero digit)

Count each space the decimal moves and that is the power of ten. If it moves to the right, it is negative (or subtracts one from n). If it moves to the left, then it is positive (or adds one to n).

Scientific Notation Operations

Addition and Subtraction

Multiplication and Division

Addition and Subtraction Procedure

• First, each power of ten must match. Do this by moving the decimal point of one number, changing the power of ten so that the number's actual value does not change.

• Add or subtract the M values and keep the same power of ten.

• Write the answer in correct scientific notation (M x 10ⁿ where M is between 1 and 10).

Multiplication and Division Procedure

• Multiply or divide the M values.

• Multiply or divide the powers of ten (which means adding or subtracting the exponents.

• Write the answer in correct scientific notation (M x 10ⁿ where M is between 1 and 10).

Direct and Inverse Proportionality

• Two quantities are directly proportional if their quotient is constant.

• Two quantities are inversely proportional if their products are constant.

• Proportions of quantities are positive.

Fill in the Blank

Which of the tables shows a direct variation?

Multiple Choice

Which of the following is written in correct scientific notation?

• $2.41\times10^{-9}$

• $24.1\times10^6$

• $2.41\times4^{10}$

• $0.241\times10^{21}$