dimensional analysis lecture 2 chapter 2. review question which of the following decimal numbers are...

Dimensional Analysis

Lecture 2Chapter 2

Review Question

• Which of the following decimal numbers are NOT written correctly for nursing charting?

A.1.2B..12C.12.0D.0.012

Calculators!!

• Bring a calculator to class• You may not use cell phones during tests• You may not borrow a calculator from another

student until they have turned in their test

Multiplication of Decimals – Without a calculator

• The decimal point in the product of decimal fractions is placed the same number of places to the left in the product, as the total number after the decimal points in the fractions multiplied.– 0.42 x 0.6 =

0.42 (2 places to the left)x 0.6 (1 place to the left) 252 (count 3 places to left) .252

0.252

Multiplication of Decimals – with a calculator

– 0.42 x 0.6 =

• Enter the number 0.42• Press the multiplication function (x)• Enter the number 0.6 • Press the equal function (=)• Write down the answer

Multiplication of Decimals – Without a calculator

• If the product contains insufficient numbers for correct placement of the decimal point, add as many zeros as necessary to the left of the product to correct this– 1.3 x 0.07

1.3 (1 place to the left)x 0.07 (2 places to the left) 91 (count 3 places to the left) .091

0.091

Multiplication of Decimals – With a calculator

– 1.3 x 0.07

Enter 1.3 Press the (x) buttonEnter 0.07Press the (=) buttonWrite down the answer

Multiplication of Decimals

• Example – 1.08 x 0.05• 1.08 (count 2 places)

x 0.05 (count 2 places) 540 (count 4 places) .0540

0.0540 (add a zero in front)

0.054 (drop extra zero)

Multiplication of Decimals

• Example – 1.08 x 0.05

– Enter 1.08 – Enter x– Enter 0.05– Press =– Write down the answer

Calculate: 0.55 x 0.2 =

A. 11B. 1.1C. 0.11D. 0.011E. None of the above


A. 0.0272B. 0.272C. 2.72D. 27.2E. None of the above


A. 0.58B. 5.8C. 58D. 580E. None of the above

Need more practice?

1. 0.55 x 0.2 2. 0.34 x 0.083. 1.16 x 0.05More problems like this on page 13 of

your text book!

Division of Decimal Fractions

0.25 = ____? _______(top #)0.125 = ____?______(bottom #)


0.25 = numerator (top #)0.125 = ____?___ (bottom #)


0.25 = numerator (top #)0.125 = denominator (bottom #)


• 3 step process1. Eliminate the decimal point2. Reduction of numbers ending in zero3. Reduction of numbers using common

denominator

• Look for which number has the must numbers to the right of the decimal – start there.

• Count how many places you have to move the decimal to the right before it is “gone”

• Move the decimal the same number of places to the other number.

• What ever you do the numerator you must do to the denominator

Eliminate the decimal point from the decimal fraction

Eliminate the decimal point from the decimal fraction

3.45 / 0.6A.345 / 6B.345 / 60C.345 / 600D.345 / 6000


• 3 step process1. Eliminate the decimal point 2. Reduction of numbers ending in zero3. Reduction of numbers using common

denominator

Reduction of numbers ending in zero

• Numbers that end in zero or zero’s may initially be reduced by crossing off the same number of zeros in both the numerator and denominator– Example

500 =20



500 = 500 =20 20



500 = 500 = 5020 20 2


• Example4200 = 4200 = 424000 4000


• Example4200 = 4200 = 424000 4000 40


• 3 step process1. Eliminate the decimal point 2. Reduction of numbers ending in zero 3. Reduction of numbers using common

denominator

Reducing fractions

• To reduce fractions, divide the numerator and the denominator by the highest common denominator (the highest number that will divide into both)– Usually 2, 3, 4, 5

Reducing fractions

Putting it all together!


• Example4200 =4000


• Example4200 = 4200 = 42 (2) = 214000 4000 40 20


• Example4200 = 4200 = 4000 4000


• Example4200 = 4200 = 42 (?)4000 4000 40


• Example4200 = 4200 = 42 (2) = 4000 4000 40


• Example4200 = 4200 = 42 (2) = 42/2 4000 4000 40 ?


• Example4200 = 4200 = 42 (2) = 42/2 = 4000 4000 40 40/2


• Example4200 = 4200 = 42 (2) = 214000 4000 40 20


• Example4200 = 4200 = 42 (2) = 21 = 1.054000 4000 40 20

Reduce the fractions as much as possible in preparation for final division

Your Turn

• Reduce the fractions as much as possible in preparation for final division

1. 40 / 16 (2) 20 / 8 (2) 10 / 4 (2) 5/22. 22 / 8 (2) 11 / 43. 66 / 8 (3) 22 / 94. 1450 / 1000 (5) 29 / 20

• More problems like this on page 15 of your text book


• 3 step process1. Eliminate the decimal point2. Reduction of numbers using common

denominator3. Reduction of numbers ending in zero

Reduce the fraction to their lowest terms in preparation for final division.

500 / 2500A.5 / 25B.1 / 5C.2 / 1D.5 / 1E.None of the above


400 / 150A.80 / 30B.4 / 15C.40 / 15D.4 / 5E.None of the above


210,000 / 600,000A.21 / 60B.2 / 6C.7 / 20D.6 / 21E.None of the above

Your turn!

• Reduce the fraction to their lowest terms in preparation for final division.

1. 500 = 500 = 5 (5) = 12500 2500 25 5

2. 400 = 400 = 40 (5) 8 150 150 15 33. 210,000 = 210,000 = 21 (3) = 7 600,000 600,000 60 20More problems on page 16 of your text

Expressing to the nearest tenth

• 1234.567– 5 is in the tenth place– 6 is in the hundredth place– 7 is in the thousandth place– . Decimal point– 4 is in the ones place– 3 is in the tens place– 2 is in the hundreds place– 1 is in the thousands place


• To express an answer to the nearest tenth, the division is carried to hundredths (2 places after the decimal). When the number representing hundredth is 5 or larger, the number representing tenths is increased by one. – Example• 1.66

– 1.7


• Example1. 1.16 – 1.2

2. 6.22– 6.3

3. 1.98– 2.0 2

Express your answer to the nearest tenths

7.598111A.7.5B.7.6C.7.50D.7.59E.7


1.454545A.1.4B.1.5C.1.45D.1.6E.1


1.838383A.1.8B.1.9C.1.7D.1.83E.2


2.976543A.2.9B.2.97C.2.8D.3.0E.3


5.038578A.5.0B.5.1C.5.03D.5.2E.None of the above

Your turn

• You did a problem on the calculator and the answer came out as follows. Express your answer to the nearest tenths.

1. 7.598111 7.62. 1.454545 1.53. 1.838383 1.94. 2.976543 3.0 35. 5.038578 5.0 5

Some harder questions?


1.12.2.013.3.000094.405.500

Some harder questions?


1.1 12.2.01 23.3.00009 34.40 405.500 500

Expressing to the nearest hundredth

• 1234.567– 5 is in the tenth place– 6 is in the hundredth place– 7 is in the thousandth place– . Decimal point– 4 is in the ones place– 3 is in the tens place– 2 is in the hundreds place– 1 is in the thousands place


• To express an answer to the nearest hundredth, the division is carried to the thousandths (3 places after the decimal point). When the number representing the thousandth is 5 or larger, the number representing the hundredths is increased by one.– Example

• 0.893 – 0.89


• Example– 0.666 • 0.67

– 0.836 • 0.84

– 0.958 • 0.96

– 0.999 • 1.0 1

Express the numbers to the nearest hundredth.



0.507

A.0.5B.0.50C.0.51D.0.57E.None of the above


3.496

A.3.5B.3.49C.3.46D.3.4E.None of the above

Your turn!• Express the numbers to the nearest hundredth.1. 1.854

– 1.852. 2.165

– 2.173. 0.507

– 0.514. 3.496

– 3.50 3.5

More problems on pg 19

Mrs. Keele, I want to be a nurse, not a

mathematician! Why do I have to learn

this? What does this have to do with

nursing?

You are to administer 3 tablets with a dosage strength of 0.04 mg each. What total dosage are

you giving?

– 3 tablets x 0.04 mg = 3 (0 places to the left)x 0.04 mg (2 places to the left) 12 mg (2 to the left) .12 mg 0.12 mg– 3 tablets x 0.04 mg = 0.12 mg

Tablets are labeled 0.2 mg and you are to give 3 ½ (3.5) tablets. What total dosage is this?

– 3.5 tablets x 0.2 mg =

3.5 (1 place)x 0.2 mg (1 place)70 mg (2 places) .7 mg 0.7 mg– 3.5 tablets x 0.2 mg = 0.7 mg

You gave 2.5 tablets labeled 0.4 mg each, and the dosage ordered was 1.2 mg. Was this the correct

dosage?• 2.5 tablets x 0.4 mg =

2.5 (1 place) x 0.4 mg (1 place) 100 (2 places) 1.00 mg 1 mg• 2.5 tablets x 0.4 mg = 1 mg• Answer the question – – No this was too little of the medication!

dimensional analysis lecture 2 chapter 2. review question which of the following decimal numbers are...

Documents

division of decimal

answer slide

product of decimal fractions

test slide

decimal points

decimal start

left x

common denominator slide