What Is a Decimal

Bristol Plymouth Practical Nurse Program

What is a Decimal?

The decimal system is based on units of 10. A decimal is similar to a fraction, but the denomonitor is always a multiple of ten.

Numbers to the Left of the decimal point are whole numbers.

Reading Decimals

The number 4378 is read as s s s s s s s e n h d d h h t t t e n e n n r d d a T O e e s d n r a T u n d s o u n u h H o u T h H T

4 3 7 8

4 thousand, three hundred and seventy eight.

Numbers to the Right of the decimal point are decimals. The rightmost column determines the ‘th place.

The number 2.5 is read as s s s s s s s e d d n h h h t t t e e n n r n d d a T O e e s d n r a u n T d s o u n u h H o u T h H T

2 and 5 tenths.

Decimals and Percentages – Hour 3 MathDecPerc.doc Bristol Plymouth Practical Nurse Program

The number 3.47 is read as s s s s s s s e n h d d h h t t t e n e n n r d d a T O e e s d n r a T u n d s o u n u h H o u T h H T

3 . 4 7

3 and 47 hundredths.

The number 12.584 is read as s s s s s s s e d d n h h h t t t e e n n r n d d a T O e e s d n r a u n T d s o u n u h H o u T h H T

1 2 . 5 8 4

12 and 584 thousandths.

Leading and Trailing Zeroes

The 1999 To Err is Human report published by the Institute of Medicine (IOM) cites the lack of a leading zero and the inclusion of a trailing decimal zero as high risks for medication error. The IOM and the Institute for Safe Medication Practice (ISMP) both recommend that DECIMALS CONTAINING NO WHOLE NUMBER MUST BE GIVEN A LEADING ZERO and that DECIMALS CONTAIN NO TRAILING ZEROES.

.5 should be written as 0.5 2.50 should be written as 2.5 .100 should be written as 0.1

In keeping with Evidenced – Based practice, the Bristol Plymouth Practical Nurse Program has adopted these guidelines. THEREFORE, WHILE AN ANSWER OF .2 MAY BE MATHMATICALLY CORRECT, THE ANSWER WILL BE MARKED WRONG. Only the correct answer of 0.2 will be accepted. SIMILARLY, AN ANSWER OF 1.250 WILL BE MARKED WRONG. Only the correct answer of 1.25 will be accepted.

Remember these Rules

Always use a leading zero for answers less than 1. Never include trailing zeroes as part of the decimal answer.

Read these Decimals

0.27 1.23 5.888

4.2 6.123 1.5

10.375 0.75 2.9

Adding Decimals

To add decimals, line up the decimal points and add each column. Be sure the answer contains the decimal point in the same place.

2.7 23.874 + 1.2 + 92.287 3.9 116.161

Sometimes you’ll need to add a trailing zero as a place holder.

2.7 23.874 + 1.0 + 92.287 3.9 116.161

2.7 23.874 + 1.0 + 92.280 3.7 116.154

Be sure there are no trailing zeroes in your final answer.

2.7 23.874 + 1.3 + 92.286 4.0 116.160

The correct answer is 4 The correct answer is 116.16

Subtracting Decimals

To subtract decimals, line up the decimal points and subtract each column. Be sure the answer contains the decimal point in the same place.

2.7 92.874 - 1.2 - 23.287 1.5 69.587

Sometimes you’ll need to add a trailing zero as a place holder.

2.7 92.874 - 1.0 - 23.287 3.9 116.161

2.7 92.874 - 1.0 - 23.280 1.7 69.594

Be sure there are no trailing zeroes in your final answer.

2.7 92.874 - 1.7 - 23.284 1.0 69.590

The correct answer is 1 The correct answer is 69.59

Always include a leading zero if the answer is less than 1.

2.7 3.874 - 1.9 - 3.284 .8 .590

The correct answer is 0.8 The correct answer is 0.59

Add and Subtract these Decimals (You may find it easier to rewrite the numbers in a column, keeping the decimal positions the same).

0.3 + 0.07 = 0.37 13.2 – 6.82 = 6.38

219.8 + 14.02 = 233.82 3.005 – 2.858 = 0.147

9.007 + 4.503 = 13.51 29 – 0.005 = 28.995

5.44 + 60.56 = 66 64.1 – 1.999 = 62.101

8.774 + 0.26 = 9.034 4.7 – 3.55 = 1.15

Multiplying Decimals

To multiply decimals, multiply the numbers as whole numbers. Insert the decimal point in the product so that the number of decimal places is equal to the total number of decimal places in the two numbers multiplied.

12.2 1 decimal point x 3.4 1 decimal point 488 1 + 1 = 2 3660 41.48 2 decimal points

3.25 1 decimal point x 4.7 2 decimal points 2275 1 + 2 = 3 13000 15.275 3 decimal points

Keep any trailing zeroes until the final number of decimal places is counted. Then, be sure to remove any trailing zeroes.

3.25 1 decimal point x 2.4 2 decimal points 1300 1 + 2 = 3 6500 7.800 3 decimal points 7.8 The correct answer is 7.8 (no trailing zeroes)

The Power of 10

Because our number system is based upon 10, numbers can be multiplied by multiples of 10 (10, 100, 1000, etc.) by simply moving the decimal point to the right by the number of 0’s in the multiplier. Fill in empty spaces with a 0.

28 * 10 10 has 1 zero, so move the decimal point one place to the right. 280

12.75 * 100 100 has 2 zeroes, so move the decimal point two places to the right. 1275

1.2345 * 1000 1000 has 3 zeroes, so move the decimal point three places to the right. 1234.5

0.123 * 100 100 has 2 zeroes, so move the decimal point two places to the right. 12.3

Multiply these Decimals (You may find it easier to rewrite these numbers in columns before multiplying.)

2.14 * 0.36 = 0.7704 2.54 * 10 = 25.4

25.5 * 1.04 = 26.52 2.2 * 100 = 220

34.82 * 1.64 = 57.1048 0.3525 * 1000 = 352.5

212.7 * 8 = 1701.6 60 * 10 = 600

35 * 2.2 = 77 4.75 * 10 = 47.5

Dividing Decimals

Before dividing by a decimal, the divisor (the divided by number) must be changed to a whole number. Count the number of spaces to move the decimal point. The dividend (the number to be divided) must have its decimal point moved that same number.

3.75 ÷ 2.5 2.5 is the divisor (the divided by number) 3.75 is the dividend (the number to be divided)

Change the divisor decimal to a whole number by Change 2.5 to 25 moving the decimal point to the right once.

Move the dividend decimal point to the right by the Change 3.75 to 37.5 same number the divisor decimal point was moved.

00.0 Set up the long division, keeping the decimal point 25 37.5 in place above the dividend.

01.5 Now do the long division.

25 37.5 25 12.5 12 5 12.0

3.75 ÷ 2.5 = 1.5

It may be necessary to add zeroes to the dividend to move the decimal point the required number of places.

3 ÷ 1.2 1.2 is the divisor (the divided by number) 3 is the dividend (the number to be divided)

Change the divisor decimal to a whole number by Change 1.2 to 12 moving the decimal point to the right once.

Move the dividend decimal point to the right by the Change 3 30 same number the divisor decimal point was moved.

00.0 Set up the long division, keeping the decimal point 12 30. in place above the dividend.

02.5 Now do the long division. 12 30.0 Add zeroes to the dividend as needed 24 60 60 0

3 ÷ 1.2 = 2.5

Dividing by Multiples of 10

To divide by 10, or a multiple of 10, move the decimal point to the left the number of zeroes in the divisor.

28 ÷ 10 10 has 1 zero, so move the decimal point one place to the left. 2.8

12345 ÷ 1000 1000 has 3 zeroes, so move the decimal point three places to the left. 12.345

Divide these Decimals (You may find it easier to set up the long division before dividing.)

2.25 ÷ 0.75 = 3 2.54 ÷ 10 = 0.254

26.4 ÷ 1.6 = 16.5 250 ÷ 100 = 2.5

32.64 ÷ 5.1 = 6.4 3525 ÷ 1000 = 3.525

212.4 ÷ 8 = 26.55 0.8 ÷ 10 = 0.08

36 ÷ 2.4 = 15 540 ÷ 100 = 5.4

Changing a Decimal to a Fraction

To change a decimal to a fraction, the number to the right of the decimal point is the NUMERATOR. The last place decimal position is the DENOMINATOR.

3 0.3 = 10

713 0.713 = 1000

Remember that all fractions must be reduced.

5 1 0.5 = reduces to 10 2

75 3 0.75 = reduces to 100 4

4 1 0.004 = reduces to 1000 250

Change these Decimals to Fractions

7 0.28 = 25

3 0.075 = 40

17 0.17 = 100

0.593 = 593 1000

1 0.05 = 20

Changing a Fraction to a Decimal

To change a fraction to a decimal, divide the NUMERATOR by the DENOMINATOR.

0.0 Set up the long division, keeping the decimal point 5 3. in place above the dividend.

0.6 Now do the long division.

5 3.0 3 0 0

3 = 0.6 5

Change these Fractions to Decimals

3 = 0.75 4

5 = 0.625 8

3 = 0.12 25

7 = 0.7 50

289 = 0.0578 5000

What is a Percentage?

Percents are parts of 100. Expressed as a fraction, the percent is the NUMERATOR. The DENOMINATOR is always 100.

33% is 33 parts of 100

33 33% is the same as 100

61 61% is the same as 100

Reduce the Fraction if necessary.

75 3 75% is the same as Reduces to 100 4

Sometimes the percent contains a decimal.

13.7% is 13.7 parts of 100

13.7 137 13.7% is the same as or 100 1000

Changing a Percent to a Decimal

To change a percent to a decimal, divide the percent by 100. To divide by 100, move the decimal point two places to the left.

25% is the same as 0.25 Move the decimal point two places to the left.

37.5% is 37.5 parts of 100

37.5% is the same as 0.375 Move the decimal point two places to the left.

Remember to remove any trailing zeroes in the decimal.

Move the decimal point two places to the left 40% is the same as 0.4 and remove the trailing zero.

Change These Percents to Decimals

58% = 0.58

72% = 0.72

12.75% = 0.1275

50% = 0.5

10.8% 0.108

Changing a Decimal to a Percent

To change a percent to a decimal, multiply the decimal by 100. To multiply by 100, move the decimal point two places to the right.

0.24 is the same as 24% Move the decimal point two places to the right.

0.275 is the same as 27.5% Move the decimal point two places to the right.

Change These Decimals to Percents

0.2 = 20%

0.78 = 78%

0.01 = 1%

0.405 = 40.5%

0.005 0.5%

Expressing a Percent as a Ratio

To express a percent as a ratio, the percent becomes the first number of the ratio, and the second number is always 100.

58% is the same as 58 : 100

62% is the same as 62 : 100

12.4% is the same as 12.4 : 100

Express these Percents as Ratios

15% = 15 : 100

27.5% = 27.5 : 100

5% = 5 : 100

Worksheet (Complete the Chart): Ratio – Fraction – Decimal – Percent Conversions

Ratio Fraction Decimal Percent

1 : 8 1 0.125 12.5% 8 12.5 : 100 is also correct

9 : 20 9 0.45 45% 20 45 : 100 is also correct

1 : 25 1 0.04 4% 25 4 : 100 is also correct

16 : 25 16 0.64 64% 25 64 : 100 is also correct

3 : 8 3 0.375 37.5% 8 37.5 : 100 is also correct

Decimals and Percentages – Hour 3 MathDecPerc.doc