Understanding Number Systems and Operations

Flashcards covering Arabic and Roman numerals, fractions, decimals, scientific notation, significant figures, measurement accuracy, exact numbers, and estimation as taught in the lecture notes.

What digits comprise the Arabic number system?

0 through 9.

Where are whole numbers located relative to the decimal point in the Arabic number system?

To the left of the decimal point; fractions are to the right.

What are the seven main symbols used in the Roman numeral system?

I, V, X, L, C, D, and M.

Where are Roman numerals sometimes used in pharmacy?

On prescriptions and medication orders.

What does the notation 'cc' stand for, and why is it discouraged?

Cubic centimeter; discouraged due to risk of misinterpretation.

What is the Roman numeral for 100?

C (or c).

If a prescription reads Disp: C tablets, how many tablets should be dispensed?

100 tablets.

What is a fraction?

A part of a whole; numerator is the top number; denominator is the bottom number.

What is the numerator in a fraction?

The top number.

What is the denominator in a fraction?

The bottom number.

When comparing fractions with the same numerator, which has the larger value?

The fraction with the smaller denominator.

When two fractions have the same denominator, which has the larger value?

The fraction with the larger numerator.

What must be created when adding or subtracting fractions with unlike denominators?

A common denominator (via equivalent fractions, multiplying by 1).

What is the purpose of creating a common denominator?

To allow addition or subtraction of fractions by expressing them with the same denominator.

What is the general method for adding fractions with different denominators?

Find the least common denominator, convert fractions to equivalent fractions, then add numerators and place over the common denominator.

What does it mean to reduce a fraction to its lowest terms?

Cancel common factors from numerator and denominator until no further reduction is possible.

If the result of adding fractions is an improper fraction, what should you do?

Convert it to a mixed number.

What are the two components of a decimal?

A whole-number component to the left of the decimal point and a fractional component to the right.

How are decimals read?

Read the whole number, then say 'and' or 'point', then read the fractional digits.

When adding or subtracting decimals, what is the key technique?

Align the decimal points in columns and pad with zeros as needed.

How do you multiply decimals?

Multiply as whole numbers; count total decimal places in factors and place the decimal in the product accordingly.

How do you divide decimals?

Move decimal points to convert divisor and dividend to whole numbers, then perform division and place the decimal in the answer.

What is rounding, and why is it important in pharmacy calculations?

Rounding simplifies numbers to keep calculations manageable; it can affect measurement accuracy.

What is scientific notation?

A way to write very large or very small numbers as a product of a number between 1 and 10 and 10 raised to a power.

What is a significant figure?

Digits that signify accuracy, including the last digit which is an estimate; the last digit is the lowest known place value.

What does an exponent indicate in scientific notation?

The power to which 10 is raised.

How do you express a number in scientific notation?

Rewrite the number as a group of significant figures multiplied by 10 with an exponent.

What are the rules for counting significant figures (Rule 1)?

Begin counting at the first nonzero digit.

What is Rule 2 in counting significant figures?

Count to the right until you reach the last significant place.

What is Rule 3 in counting significant figures?

Zeros between digits are significant.

What is Rule 4 in counting significant figures?

Leading zeros are not significant; they only mark the decimal position.

What is Rule 5 in counting significant figures?

Trailing zeros may or may not be significant, depending on precision.

What is measurement accuracy?

The degree to which a measurement matches the actual value.

How can measurement accuracy be expressed?

As the number of significant figures or as a percent; also as an accuracy range.

What is the accuracy range?

The upper and lower limits that a value can be measured.

What is an example of an item weighed with a balance to the nearest tenth of a milligram, and how many significant figures does it have?

If the scale is only accurate to tenths, the measurement 1.459 mg has two significant figures (the 5 and 9 are not significant). The value should be reported as 1.5 mg.

What is an exact number in pharmacy?

Counts of items (e.g., number of tablets or days) that have no uncertainty; only measured quantities have significant figures.

What is estimation?

The process of finding an approximate answer before calculation to verify reasonableness.

What is the purpose of estimating sums and differences?

Round numbers and then add or subtract; ignore the digits in the ones place and below.

What is the rule for estimating products and quotients?

Round each number; for multiplication, temporarily drop trailing zeros; for division, drop zeros from the divisor and adjust the dividend accordingly.

What is the estimated product of 325 × 618?

180,000 (rough estimate; actual product is 200,850).

Why is estimating a drug dose useful?

To verify the accuracy of the calculated dose; if the estimate is not close, recheck.

What does 'Using Exact Numbers' mean in pharmacy calculations?

Counts (like number of tablets) are exact numbers with no uncertainty; only measured quantities have significant figures.

How is the decimal 2.375 commonly read?

Two point three seven five.

How would you write 6,500 in scientific notation?

6.5 × 10^3.