Decimals, Fractions and Percentages

Decimals, Fractions and Percentages are just different ways of showing the same value:

A Half can be written...

As a fraction:	1/2
As a decimal:	0,5
As a percentage:	50%

A Quarter can be written...

As a fraction:	1/4
As a decimal:	0,25
As a percentage:	25%

Here is a table of commonly used values shown in Percent, Decimal and Fraction form:Example Values

Percent	Decimal	Fraction
1%	0,01	1/100
5%	0,05	1/20
10%	0,1	1/10
12½%	0,125	1/8
20%	0,2	1/5
25%	0,25	1/4
331/3%	0,333...	1/3
50%	0,5	1/2
75%	0,75	3/4
80%	0,8	4/5
90%	0,9	9/10
99%	0,99	99/100
100%	1
125%	1,25	5/4
150%	1,5	3/2
200%	2

Para practicar

Problems and exercises

DECIMALS

Definition:

A decimal is any number in our base-ten number system. Specifically, we will be using numbers that have one or more digits to the right of the decimal point. The decimal point is used to separate the ones place from the tenths place in decimals. As we move to the right of the decimal point, each number place is divided by 10.

Mixed Number	------------- E x p a n d e d F o r m ------------		Decimal Form
	= (5 x 10) + ( 7 x 1)	+ (4 x ) + (9 x )	= 57.49

As you can see, it is easier to write

in decimal form. Let's look at this decimal number in a place-value chart to better understand how decimals work.

PLACE VALUE AND DECIMALS

	5	7	.	4	9

As we move to the right in the place value chart, each number place is divided by 10. For example, thousands divided by 10 gives you hundreds. This is also true for digits to the right of the decimal point. For example, tenths divided by 10 gives you hundredths. When reading decimals, the decimal point should be read as "and." Thus, we read the decimal 57.49 as "fifty-seven and forty-nine hundredths." Note that in daily life it is common to read the decimal point as "point" instead of "and." Thus, 57.49 would be read as "fifty-seven point four nine." This usage is not considered mathematically correct.

Example 1: Write each phrase as a fraction and as a decimal.

phrase	fraction	decimal
six tenths		.6
five hundredths		.05
thirty-two hundredths		.32
two hundred sixty-seven thousandths		.267

So why do we use decimals?

Decimals are used in situations which require more precision than whole numbers can provide. A good example of this is money: Three and one-fourth dollars is an amount between 3 dollars and 4 dollars. We use decimals to write this amount as $3.25.A decimal may have both a whole-number part and a fractional part. The whole-number part of a decimal are those digits to the left of the decimal point. The fractional part of a decimal is represented by the digits to the right of the decimal point. The decimal point is used to separate these parts. Let's look at some examples of this.

decimal	whole-number part	fractional part
3.25	3	25
4.172	4	172
25.03	25	03
0.168	0	168
132.7	132	7

Let's examine these decimals in our place-value chart.

PLACE VALUE AND DECIMALS

			3	.	2	5
			4	.	1	7	2
		2	5	.	0	3
			0	.	1	6	8
	1	3	2	.	7

Note that 0.168 has the same value as .168. However, the zero in the ones place helps us remember that 0.168 is a number less than one. From this point on, when writing a decimal that is less than one, we will always include a zero in the ones place. Let's look at some more examples of decimals.

Example 2: Write each phrase as a decimal.

Phrase	Decimal
fifty-six hundredths	0.560
nine tenths	0.900
thirteen and four hundredths	13.040
twenty-five and eighty-one hundredths	25.810
nineteen and seventy-eight thousandths	19.078

Example 3: Write each decimal using words.

Decimal	Phrase
0.0050	five thousandths
100.6000	one hundred and six tenths
2.2800	two and twenty-eight hundredths
71.0620	seventy-one and sixty-two thousandths
3.0589	three and five hundred eighty-nine ten-thousandths

It should be noted that five thousandths can also be written as zero and five thousandths.

Expanded Form

We can write the whole number 159 in expanded form as follows: 159 = (1 x 100) + (5 x 10) + (9 x 1). Decimals can also be written in expanded form. Expanded form is a way to write numbers by showing the value of each digit. This is shown in the example below.

Example 4: Write each decimal in expanded form.

Decimal		Expanded form
4.1200	=	(4 x 1) + (1 x ) + (2 x )
0.9000	=	(0 x 1) + (9 x )
9.7350	=	(9 x 1) + (7 x ) + (3 x ) + (5 x )
1.0827	=	(1 x 1) + (0 x ) + (8 x ) + (2 x ) + (7 x )