2.1: Understanding Decimals
 Page ID
 7086
Numbers written with decimals is another way of expressing fractions. However, decimals have a distinct differentiation with fractions in that decimals are based on 10. In that, one decimal place to the right of the whole number indicates tenths, two decimal places to the right of the whole number indicates hundredths, three decimal places to the right of the whole number indicates thousandths, etc.
Example \(\PageIndex{1}\)
0.1 = tenths place
1.01 = hundredths place
0.001 = thousandths place
1.01 = ten thousandths place
Decimals can easily be written as fractions by using the number to the right of the decimal point as the numerator and then using a 10, 100, 1,000, 10,000, etc. as the denominator. Determining which “baseten” number to use as the denominator is determined by the number of digits there are to the right of the decimal point.
Example \(\PageIndex{2}\)
\(\begin{array}{ll}
0.1 \rightarrow \dfrac{1}{10} & 1 \text { tenth } \\
0.01 \rightarrow \dfrac{1}{100} & 1 \text { hundredth } \\
0.001 \rightarrow \dfrac{1}{1,000} & 1 \text { thousandth } \\
0.0001 \rightarrow \dfrac{1}{10,000} & 1 \text { tenthousandth }
\end{array}\)
Exercise 2.1
Write the following decimals as fractions and reduce if necessary.
 0.2 =
 0.103 =
 0.13 =
 0.02 =
 0.1234 =
 0.0023 =
 0.0101 =
 0.1010 =
 0.020 =
 0.0202 =
 0.1000 =
 0.4500 =
Exercise 2.1.1
Write the following expressions as decimals and fractions.
Decimal 
Fraction 


7 tenths 


1,000 tenthousandths 


475 thousandths 


32 hundredths 


12 thousandths 


2,345 tenthousandths 


3 hundredths 


10 thousandths 


132 tenthousandths 


4,002 tenthousandths 
Digits to the left of the decimal indicate a whole number. Whenever there is a whole number with a decimal fraction the expression is pronounced using “and.”
Example:
12.3 = Twelve and three tenths = \(12 \dfrac{3}{10}\)
100.07 = One hundred and seven hundredths = \(100 \dfrac{7}{100}\)
3,005.023 = Three thousand five and twentythree thousandths = \(3,005 \dfrac{23}{1,000}\)
Exercise 2.1.2
Write the following expressions as a decimal and a fraction. Remember to reduce if necessary.
Decimal 
Fraction 


Two and five hundredths 


Thirteen and two hundred thousandths 


One thousand three and two tenthousandths 


Fiftyfive and fifty hundredths 


One and fourteen hundredth 


Eleven thousand four and twelve thousandths 


Ten and two tenths 


Four hundred one and four tenthousandths 


Five thousand two hundred eight and one thousand tenthousandths 