### 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, # 12.95732 # has exactly #5# decimal places .

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