Numbers: Ratios
Decimal numbers
So far, we have seen integers and fractions. Now we will look at decimal numbers. Decimal numbers are a regular occurrence; for example, amounts of money are often written as a decimal number with #2# decimals.
A decimal number is a number with a decimal point.
The numbers to the right of the decimal point are called digits.
For example, #4.15# is a decimal number with #2# digits, which occupy decimal places.
The digits indicate what part is still added to the integer. For example, #4.15# indicates that we add #\tfrac{15}{100}# to #4#.
Examples
#32.1#
#301.102#
#5.18#
#6.20335#
#18.2#
For the integer #1258#, we say that it consists of:
#1# thousand
#2# hundreds
#5# tens
#8# ones
The value of #1258# is therefore: \[1 \times 1000+2 \times 100+5\times 10 + 8 \times 1\]
Similarly, the decimal number #0.1258# consists of:
#0# ones
#1# tenth
#2# hundredths
#5# thousandths
#8# ten thousandths
The value of #0.1258# is therefore: \[0\times 1+1 \times 0.1 + 2 \times 0.01 + 5 \times 0.001 + 8 \times 0.0001\]
Examples
The decimal places are the places after the decimal point. In this case, # 2.9783 # has exactly #4# decimal places .
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