Contents
Decimal Fractions:
Fractions such as \(\frac{7}{10}\) can be written as .7 or 0.7. We call .7 a decimal fraction or decimal.
Let us consider the place values of digit 1 in different places of the place value table.
|
In Thousands place |
In Hundreds place |
In Tens place |
In Ones place |
In Tenths place |
In Hundredths place |
In Thousandths place |
|
|
Place Value of Digit 1 |
1000 |
100 |
10 |
1 |
\(\frac{1}{10}\) |
\(\frac{1}{100}\) |
\(\frac{1}{1000}\) |
So, 12 tenths = l0 tenths + 2 tenths = 1 one + 2 tenths
34 hundredths = 30 hundredths + 4 hundredths = 3 tenths + 4 hundredths
49 thousandths = 40 thousandths + 9 thousandths = 4 hundredths + 9 thousandths.
What is 3/5 as a decimal?
Writing and Reading Decimal Fractions:
When writing a fraction with a denominator like 10, 100, 1000 or 10000:
To position the decimal point correctly. you may have to fill in zeros as shown below.
\(\frac{2}{10}\) = 0.2 Zeros in the denominator = 1. Position of the point = 1 + 1 = 2nd from the right.
\(\frac{6}{100}\) = 0.06 Zeros in the denominator = 2. Position of the point = 1 + 2 = 3rd from the right.
\(\frac{9}{1000}\) = 0.009 Zeros in the denominator = 3. Position of the point = 1 + 3 = 4th from the right.
\(\frac{4}{100}\) = 0.04 read as point zero four.
\(\frac{56}{1000}\) = 0.056 read as zero point zero five six.
\(\frac{91700}{10000}\) = 9.17 nine point one seven.
Mixed fractions can be written as decimals as shown below.
\(12\frac{2}{10} = \frac{122}{10} \) = 12.2
\(5\frac{39}{100} = \frac{539}{100}\) = 5.39
\(4\frac{287}{10000} = \frac{40287}{10000}\) = 4.0287
Like a mixed fraction, a decimal number has two parts: an integral part and a fractional or decimal part.
For example, in 13.21, the integral part is 13 and the decimal part is .21.
in 0.36, the integral part is 0 and the decimal part is .36.
Place Values in Decimals:
In the decimal system of numbers, the place value of a digit gets multiplied by 10 as we move left or divided by 10 as we move right.
For example, 782.4961 = 7 hundreds + 8 tens + 2 ones + 4 tenths + 9 hundredths + 6 thousandths + 1 ten thousandths
= 7 x 100 + 8 x 10 + 2 x 1 + \(\frac{4}{10}\) + \(\frac{9}{100}\) + \(\frac{6}{1000}\) + \(\frac{1}{10000}\)
= 700 + 80 + 2 + .4 + .09 + .006 + .0001
782.4961 can be shown on a place-value chart as:
Conversion:
Decimal Fractions into Decimal Numbers:
A decimal fraction can be converted into a decimal number (or simply called a decimal) using a decimal point.
For converting a decimal fraction into a decimal number, write the numerator of the fraction and put the decimal point after as many digits from the right as the number of zeros in the denominator.
For example, \(\frac{26}{10}\) has one zero in the denominator. So, \(\frac{26}{10}\) = 2.6
\(\frac{115}{100}\) has two zeros in the denominator. So, \(\frac{115}{100}\) = 1.15
\(\frac{2235}{1000}\) has three zeros in the denominator. = 2.235 and so on.
Here, 2.6, 1.15 and 2.235 are called decimal numbers or decimals.
Decimal Numbers into Decimal Fractions:
A decimal number can also be converted into a decimal fraction.
For converting a decimal number into a decimal fraction, write the number without a decimal point to form the numerator of the fraction. Write 1 followed by as many zeros as the decimal places, to form the denominator of the fraction.
For example, 1.3 has one decimal place. So, 1.3 = \(\frac{13}{10}\)
4.62 has two decimal places. So, 4.62 = \(\frac{462}{100}\)
6.275 has three decimal places. So, 6.275 = \(\frac{6275}{1000}\) and so on.
Points to Remember while converting a decimal fraction into a decimal number or vice versa:
For example, in the decimal number 2.67, 2 is a whole number and .67 is a fraction.
For example, the whole number 7 can be written as 7.0 or 7.00 and so on.
For example, .725 is written as 0.725.
For example, 5.2 is same as 05.2 or 005.2, etc.
For example, 1.3 is same as 1.30 or 1.300 and so on.