Naming DecimalsTenths as Decimals

Decimals are a method of writing fractional numbers without writing a fraction having a numerator and denominator.

The fraction 7/10 could be written as the decimal 0.7. The period or decimal point indicates that this is a decimal.

The decimal 0.7 could be pronounced as SEVEN TENTHS or as ZERO POINT SEVEN.

If a decimal is less than 1, place a zero before the decimal point. Write 0.7 not .7

Tenths as Decimals

There are other decimals such as hundredths or thousandths. They all are based on the number ten just like our number system.

A decimal may be greater than one. The decimal 3.7 would be pronounced as THREE AND SEVEN TENTHS.

HUNDREDTHS The fraction 37/100 could be written as the decimal 0.37. The

period or decimal point indicates that this is a decimal.

The decimal 0.37 could be pronounced as THIRTY-SEVEN HUNDREDTHS or as ZERO POINT THREE SEVEN or ZERO POINT THIRTY-SEVEN.

A decimal may be greater than 1. The decimal 12.37 could be pronounced as TWELVE AND THIRTY-SEVEN HUNDREDTHS or as TWELVE POINT THIRTY-SEVEN.

Thousandths Thousandths follow a similar pattern. They have three digits

after the decimal point. The decimal 0.749 is pronounced "seven hundred forty-nine thousandths" or "zero point seven forty-nine".

There may be zeros after the decimal point. The decimal 0.064 is pronounced "sixty-four thousandths" or "zero point zero sixty-four".

A decimal number may be larger than 1. The word and may be

used to indicate the decimal point so it should not be used in other parts of the name of the decimal. The decimal 234.987 could be pronounced Two hundred thirty-four AND nine hundred eighty-seven thousandths.

TEN THOUSANDTHSTEN-THOUSANDTHS HAVE FOUR DIGITS

AFTER THE DECIMAL POINT.

ADDITION OF DECIMALS

• Decimals are fractional numbers. The decimal 0.3 is the same as the fraction 3/10. The number 0.78 is a decimal that represents 78/100.

• Adding Decimals is just like adding other numbers. • Always line up the decimal points when adding

decimals. • Remember to put the decimal point in the proper

place in your answer.

Subtracting Decimals

Subtracting Decimals is just like subtracting other numbers.

Always line up the decimal points when subtracting decimals.

Remember to put the decimal point in the proper place in your answer

MULTIPLYING HOW TO MULTIPLY A THREE DIGIT DECIMAL BY A ONE DIGIT

DECIMAL NUMBER (FOR EXAMPLE 0.529 * 0.7):

PLACE ONE DECIMAL ABOVE THE OTHER SO THAT THEY ARE LINED UP ON THE RIGHT SIDE. DRAW A LINE UNDER THE BOTTOM NUMBER. TEMPORARILY DISREGARD THE DECIMAL POINTS AND MULTIPLY THE NUMBERS LIKE MULTIPLYING A THREE DIGIT NUMBER BY A ONE DIGIT NUMBER.

0.529 0.7

Rounding To the Nearest Hundredth Rounding decimals is very similar to rounding other

numbers. If the thousandths place of a decimal is four or less, it is dropped and the hundredths place does not change. For example, rounding 0.843 to the nearest hundredth would give 0.84.

If the thousandths place is five through nine, the hundredths place is increased by one. The decimal 0.846 rounded to the nearest hundredth is 0.85.

Rounding To the Nearest Tenth

• Rounding decimals is very similar to rounding other numbers. If the hundredths and thousandths places of a decimal is forty-nine or less, they are dropped and the tenths place does not change.

• For example, rounding 0.843 to the nearest tenth would give 0.8.

• If the hundredths and thousandths places are fifty or more, the tenths place is increased by one. The decimal 0.866 rounded to the nearest tenth is 0.9

Rounding Decimals

• 27.17469 rounded to the nearest whole number is 27 36.74691 rounded to the nearest whole number is 37 12.34690 rounded to the nearest tenth is 12.3 89.46917 rounded to the nearest tenth is 89.5 50.02139 rounded to the nearest hundredth is 50.02 72.63539 rounded to the nearest hundredth is 72.64 46.83531 rounded to the nearest thousandth is 46.835 9.63967 rounded to the nearest thousandth is 9.640

• Rules for rounding decimals. 1. Retain the correct number of decimal places (e.g. 3 for thousandths, 0 for whole numbers) 2. If the next decimal place value is 5 or more, increase the value in the last retained decimal place by 1.

Place Values of Decimals

• Decimal numbers, such as O.6495, have four digits after the decimal point. Each digit is a different place value.

• The first digit after the decimal point is called the tenths place value. There are six tenths in the number O.6495.

• The second digit tells you how many hundredths there are in the number. The number O.6495 has four hundredths.

• The third digit is the thousandths place. • The fourth digit is the ten-thousandths place which is five

in this example. • Therefore, there are six tenths, four hundredths, nine

thousandths, and five ten-thousandths in the number 0.6495.

Comparing Decimal Numbers

• If there are two decimal numbers we can compare them. One number is either greater than, less than or equal to the other number.

• A decimal number is just a fractional number. Comparing 0.7 and 0.07 is clearer if we compared 7/10 to 7/100. The fraction 7/10 is equivalent to 70/100 which is clearly larger than 7/100.

• Therefore, when decimals are compared start with tenths place and then hundredths place, etc. If one decimal has a higher number in the tenths place then it is larger than a decimal with fewer tenths. If the tenths are equal compare the hundredths, then the thousandths etc. until one decimal is larger or there are no more places to compare. If each decimal place value is the same then the decimals are equal.

Ordering Decimal Numbers• Numbers have an order or arrangement. The number two is between

one and three. Three or more numbers can be placed in order. A number may come before the other numbers or it may come between them or after them.

• Example: If we start with the numbers 4.3 and 8.78, the number 5.2764 would come between them, the number 9.1 would come after them and the number 2 would come before both of them.

• Example: If we start with the numbers 4.3 and 4.78, the number 4.2764 would come before both of them, the number 4.9 would come after them and the number 4.5232 would come between them.

• The order may be ascending (getting larger in value) or descending (becoming smaller in value).

Percent of a Number• To determine the percent of a number do the

following steps:• Multiply the number by the percent (e.g. 87 * 68 =

5916)• Divide the answer by 100 (Move decimal point two

places to the left) (e.g. 5916/100 = 59.16)• Round to the desired precision (e.g. 59.16 rounded

to the nearest whole number = 59)

Finding Percent

• Example: 68 is what percent of 87?• Divide the first number by the second (e.g. 68 ÷ 87

= 0.7816)• Multiply the answer by 100 (Move decimal point

two places to the right) (e.g. 0.7816*100 = 78.16)• Round to the desired precision (e.g. 78.16 rounded

to the nearest whole number = 78)• Follow the answer with the % sign (e.g. 68 is 78% of

87)

FRACTIONS AND DECIMALS• Decimals are a type of fractional number. The decimal 0.5 represents

the fraction 5/10. The decimal 0.25 represents the fraction 25/100. Decimal fractions always have a denominator based on a power of 10.

• We know that 5/10 is equivalent to 1/2 since 1/2 times 5/5 is 5/10. Therefore, the decimal 0.5 is equivalent to 1/2 or 2/4, etc.

• Some common Equivalent Decimals and Fractions: 0.1 and 1/10• 0.2 and 1/5• 0.5 and 1/2• 0.25 and 1/4• 0.50 and 1/2• 0.75 and 3/4• 1.0 and 1/1 or 2/2 or 1

Converting a Fraction to a Decimal

• Do the following steps to convert a fraction to a decimal:For example: Convert 4/9 to a decimal.

• Divide the numerator of the fraction by the denominator (e.g. 4 ÷ 9=0.44444)

• Round the answer to the desired precision.

CONVERTING A FRACTION TO A PERCENT

• Do the following steps to convert a fraction to a percent:For example: Convert 4/5 to a percent.

• Divide the numerator of the fraction by the denominator (e.g. 4 ÷ 5=0.80)

• Multiply by 100 (Move the decimal point two places to the right) (e.g. 0.80*100 = 80)

• Round the answer to the desired precision.• Follow the answer with the % sign (e.g. 80%)

Converting a Percent to a Fraction

• Do the following steps to convert a percent to a fraction:For example: Convert 83% to a fraction.

• Remove the Percent sign• Make a fraction with the percent as the numerator

and 100 as the denominator (e.g. 83/100)• Reduce the fraction if needed