Week 2 Decimals and Percents

What are decimal numbers?• The value of a decimal number depends on the

place or location of each digit, and the decimal point is used to express fractions.

• For example, 123 means one hundred twenty-three, but 321 means three hundred twenty-one (the order of the digits tells us what they represent).

• Digits AFTER the decimal point express tenths, hundredths and thousandths, for example, 1.4 means one and 4 tenths; 1.04 means one and 4 hundredths and 1.004 means one and 4 thousandths

How are decimal numbers read?

• The numbers after the decimal point are expressed as fractions of 10, 100, or 1000.

• For example, 12.46 is read as “twelve and 46 hundredths”.

• 0.111 is “zero and one hundred and eleven thousandths”.

• 1.2 is “one and two tenths”.• Often decimals will also be read using the word

“point” for the decimal point, for example 1.2 is “one point two” and 0.111 is “zero point one one one”.

Test Yourself• What is the decimal number for “twenty-eight

thousandths”?• 0.028• What is the decimal number for “two thousand

and 55 hundredths”?• 2000.55• What is the decimal number for “six tenths”?• 0.6• What is the decimal number for “five hundred

sixteen point zero six”?• 516.06

Uses of Decimal Numbers in Pharmacy•One of the most obvious uses of decimal

numbers in pharmacy --- MONEY !!!•Many drug doses and volumes are

expressed as decimal numbers, for example, you may need to add 5.2 ml of a drug to an IV bag, or split a tablet to get a 0.5 mg dose for a patient.

•You will use decimal numbers frequently and need to work comfortably with them.

Make sure to remember • Do not use trailing zeroes in pharmacy practice ---

they can cause serious errors.• For example, write 4 mg , NOT 4.0 mg. If the

decimal point is missed, the number could be mistaken for 40 and the dose would be 10 times too large.

• In the pharmacy, for any decimal number less than 1, always use a leading zero.

• For example, write 0.4mg, NOT .4mg. If the decimal point is missed, the number could be mistaken for 4 and the dose would be 10 times too large.

Test Yourself• Are these written correctly?• 1.0• No (do not use trailing zero after the decimal

point)• 16• Yes• 0.24• Yes• .6• No (always use a leading zero before the

decimal point)

Test Yourself• This number is written incorrectly. What could

it be mistaken for? How serious would that error be?

.500 Could be mistaken for 500There is no leading zero before the decimal point, and 2 trailing zeroes after the decimal point.This would be a thousand-fold error (500 is one thousand times 0.5) and would be a FATAL error for many drugs.The correct way to write this number is 0.5

Rounding Decimal Numbers• Rounding of decimal numbers may be required since

measuring devices in the pharmacy are not always as precise as the calculated dose or volume.

• For example, you might have an order for 6.78ml of a suspension, but a syringe to measure it in that is only accurate to tenths of a milliliter.

• To round to tenths, find the rounding digit (the tenths place, or “7” in the above example).

• Look at the digit just to the right of the rounding digit (“8” in this example).

• If it is 0-4, round down. If it is 5-9, round up.• Since “8” falls in the category 5-9, we will round up the

“7” in the tenths place to “8” to give 6.8ml.

Rounding Decimal Numbers•Another example:•Round 0.421 mg to the nearest hundredth.•The rounding digit will be the digit in the

hundredths place (“2”)•The number just to the right of the rounding

digit is “1”•Since “1” falls in the category 0-4, we will

round down.•The rounding digit will remain a “2” and the

answer will be 0.42 mg.

Test Yourself

•Round to the nearest tenth: 0.24•0.2•Round to the nearest tenth: 0.25•0.3•Round to the nearest tenth: 2.4013•2.4•Round to the nearest tenth: 2.4678•2.5

Test Yourself• Round to the nearest hundredth: 0.1677• 0.17• Round to the nearest hundredth: 2.555• 2.56• Round to the nearest whole number: 35.5• 36• You have an IV label asking for you to draw up

2.82 ml of a drug and the smallest syringe on hand is a 3ml syringe marked in tenths of a ml. How much will you draw up? (round to tenths)

• 2.8 ml

Adding and Subtracting Decimal Numbers• When adding or subtracting decimal numbers,

be sure to align the numbers so that the decimal points are all in a vertical line.

• For example, 0.2 + 1.45 + 23 = ? 0.2 1.45 + 23.0 _____ 24.65Most often in practice, you will be using a calculator to add and subtract decimals.

Test Yourself

•Subtract these decimal numbers on paper. Check your answer using a calculator.

•235.6 – 14.44 = ?

235.6 - 14.44_______ 221.16

Multiplying Decimal Numbers• When decimal numbers are multiplied, first

multiply as if they are whole numbers, then put the same number of decimal places in the answer as the TOTAL number of decimal places in the two numbers that were multiplied together.

• For example, 0.5 x 0.2 = 0.5x 0.2____ 5 x 2 = 10; total no. of decimal places is 2 0.10

Dividing Decimal Numbers

If the divisor is a whole number, then do division as if both numbers are whole numbers, and move the decimal point in the final answer to the left the same number of places as in the dividend. dividend ÷ divisor = quotient

For example: 24.4 ÷ 4 = ? 244 ÷ 4 = 61 (divide as whole numbers) The dividend had one decimal place, so move decimal place in 61 one place to the left. Final answer is 6.1.

If the divisor is not a whole number, multiply it by a power of 10 to get a whole number, and also multiply the dividend by that same power of 10. Then divide.

For example, 24.4 ÷ 0.4 = ?24.4 (10) ÷ 0.4 (10) = 244 ÷ 4 = 61 no further movement of decimal place needed

Multiplying and Dividing Decimal Numbers• In practice, you will most often be using a

calculator to multiply and divide decimal numbers in the pharmacy.

•Try these problems on paper and check your answer using a calculator.

•5.5 x 2.2 = ?•55 x 22 = 1210 (remove decimals and

multiply)•Answer is 12.10 (put same number of decimal

places in the answer as the total number in the two multipliers)

Test Yourself• Try on paper and check your answers with a

calculator.• 50.5 ÷ 25 = ?• 505 ÷ 25 = 20.2 (divisor is a whole number, so first

divide as whole numbers)• Final answer is 2.02 (move the decimal in the

answer above to the left by the number of places in the dividend)

• 50.5 ÷ 0.25 = ?• Divisor is a decimal, so multiply it by 100 to make it a

whole number. Also multiply the dividend by 100.• 50.5 (100) ÷ 0.25 (100) = 5050 ÷ 25 = 202

To Remember about Decimal Numbers• Decimal numbers express numbers as multiples and

fractions of 10, e.g. thousands, hundreds, tens, ones, tenths, hundredths, thousandths.

• Calculations involving decimal numbers are usually done on a calculator in the pharmacy.

• Trailing zeroes after the decimal point can lead to errors and should be avoided.

• Leading zeroes before the decimal point in a number less than one are a good practice to avoid errors.

• To round a decimal number, find the rounding digit. If the first number after the rounding digit is 0-4, round down. If the first number after the rounding digit is 5-9, round up.

Percents

•Percents are fractions with a denominator of 100.

•For example, 20% = 20/100 0.5% = 0.5/100•Percents can also be expressed as a

decimal number. Express the percent as a fraction, then divide.

•For example, 20% = 20/100 = 0.2 0.5%= 0.5/100 = 0.005

Percents• When converting percents to a decimal, you can use a

calculator, or you can remember this shortcut: simply move the decimal point two places to the left.

• For example, 111% = 111/100 = 1.11 (divided on a calculator) or take 111 (same as 111.0) and move decimal two places to the left = 1.110 = 1.11.

• To convert a decimal to a percent, multiply by 100. For example, 0.12 = ? %

• 0.12 x 100 = 12 Answer is 12%• Any fraction can be expressed as a percent by dividing

to get a decimal number, and then multiplying by 100.• ¾ = 0.75 0.75 x 100 = 75%

Test Yourself

•16.5% = ? / 100•16.5•Express 0.25% as a decimal.•0.25% = 0.25/100 = 0.0025•Express 0.025 as a percent.•0.025 x 100 = 2.5%•Express as a percent: 5/6•5/6 = 0.833 = 83.3%

Percents

•To find a certain percent of a number, express the percent as a decimal number or a fraction and then multiply.

•30% of 90 = ?•(30/100) x 90 = 27 or 0.3 x 90 = 27•0.1% of 12 = ?•(0.1/100) x 12 = 0.012 or o.oo1 x 12 =

0.012

Test Yourself• What is 100% of 600?• (100/100) x 600 = 600 or 1 x 600 = 600• 100% of something is all of it !• What is 12.2% of 89?• (12.2/100) x 89 = 10.858 or 0.122 x 89 = 10.858• An item in the pharmacy is on sale at 40% off. The

regular price is $1.89. What is the sale price?• 40% of $1.89 = 0.40 x $1.89 = $0.756 (round to

$0.76)• Sale price is $1.89 – $0.76 off = $ 1.13

Percents

•How to find what percent one number is of another: express as a fraction and convert to a percent by dividing

•For example: 2 is what percent of 3?•2 of 3 = 2/3 = 0.67•0.67 x 100 = 67%•So 2 is 67 % of 3.

Test Yourself

•The pharmacy had 100 bottles of acetaminophen 325mg tablets on hand yesterday, but today, only 36 bottles remain. What percent was sold?

•100 – 36 = 64 bottles sold.•64 out of 100 is 64/100 = 0.64•0.64 x 100 = 64% sold

To Remember about Percents• Percents can be expressed as fractions of 100.• Percents can be expressed as decimal numbers,

either by using a calculator, or moving the decimal place two places to the left.

• Any decimal number can be expressed as a percent by multiply it by 100.

• Any fraction can be expressed as a percent by dividing it to get a decimal number, then multiplying by 100.

• To find a percentage of a number, convert the percent to a decimal number or fraction, then multiply.

Next Steps• Do the homework problems and check your answers

in the back of the textbook.• Do the discussion board assignment and also post

any observations or questions you might have about this lesson to the discussion board.

• Review this powerpoint and the homework problems before taking this week’s quiz.

• The material from last week and this week should be review material and we will be quickly moving into more involved pharmacy math. If you do not feel comfortable with these two lessons, please contact me immediately.