DecimalsDecimalsBy: Sandy DensonBy: Sandy Denson

Table of ContentsTable of Contents

• Place Value 2,3• Writing Decimals as Fractions 4,5• Writing Fractions as Decimals 6,7• Comparing Decimals 8• Adding and Subtracting Decimals 9• Multiplying Decimals by Decimals 10• Multiplying Decimals by 10, 100, 1000 11• Dividing Decimals 12

Place Value ChartPlace Value Chart

1 3 . 4 5 62

Hundreds

Tens

Ones

Decimal Point

Tenths

Hundredths

Thousandths

123.456

One hundred twenty-three and four hundred fifty-six thousandths

Remember:Remember:

.Hundreds Tens Ones Tenths Hundredths

Thousandths

Three hundred fifty-seven and six hundred forty-two thousandths

5 7 . 6 4 23

When writing or saying numbers with decimal parts, we must say “ths” at the end of the ten, hundred, and thousand that is on the right side of the decimal point.

Writing Decimals as Writing Decimals as FractionsFractions

When we read the decimal number, we automatically know what the denominator of our fraction is going to be. Our numerator of the fraction is going to be the number we say. For example 0.5, we say this as five tenths. Therefore when we write our fraction it will have a denominator of 10 and a numerator of 5.

5/10

Writing Decimals as Writing Decimals as FractionsFractions

0.4 4/10

0.6 6/10

0.05 5/100

0.21 21/100

0.007 7/1000

0.675 675/1000

Writing Fractions as Writing Fractions as DecimalsDecimals

By reading the fraction out loud, it lets us know what place value we are going to write our decimal number to. For example: 23/100 We read this fraction as twenty-three hundredths. We know that hundredths has two decimal places. Therefore, we must have two places to the right of the decimal.

0.23

Writing Fractions as Writing Fractions as DecimalsDecimals

5/10 0.5

9/10 0.9

12/100 0.12

7/100 0.07

139/1000 0.139

3/1000 0.003

Comparing DecimalsComparing Decimals

12.345 13.675

=

<

When comparing decimals, the first thing to do is to compare the whole numbers first. Whatever side is larder, will be the larger number.

Therefore in this problem, we would say that 12.345 is less than 13.675.

Adding and Subtracting Adding and Subtracting DecimalsDecimals

The most important thing to remember when adding or subtracting decimals is to keep the decimal points all lined up vertically. In order to do this, we must write the problem vertically and not horizontally. In order to keep the decimals lined up, you can add zeros to the numbers to keep them equal in digits. For example:

0.303

+4.230

4.533

Multiplying Decimals by Multiplying Decimals by DecimalsDecimals

When multiplying decimals, we do not need to line up the decimal points before we work the problem. We need to multiply the problem as if we were multiplying whole numbers. After we have the problem worked, we need to count all the places to the right of each decimal point. Then, that is the amount of places we put in the answer. For example:12.3 x 1.5 = ???

12.3

X 1.5

613

+1230

18.45

As we see, we have one place to the right of each number. We add them up, and we have two decimal places. Therefore, our answer must have two decimal places in it.

Multiplying Decimals by Multiplying Decimals by 10, 100, 100010, 100, 1000

In our number system, the places have value. The value of each place is 10 times greater each time we move one place to the left. When we multiply a number by 10, the digits all shift one place to the left. When we multiply 0.34 by 10, the three shifts from the tenths place to the ones’ place, and the four shifts from the hundredths place to the tenths place.

0.34

3.4

Dividing Decimals by Dividing Decimals by DecimalsDecimals

When dividing a decimal number by a decimal number, we move the decimal point of the divisor so that it becomes a whole number. Then we move the decimal point in the dividend the same number of places. The decimal point in the quotient is straight up from the new location of the decimal point in the division box. The memory cue for dividing by a decimal number is “over, over, and up.” For example:

0.3 0.12

3 1 . 2 0.4

1 2

DecimalsDecimals

Sandy Denson, 2003Sandy Denson, 2003

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