Expanded form of decimals

 

   Recall that a whole number such as 73 486 has 5 digits and the place value table for the whole number is as follows:

Place value table from units to ten million.

http://www.mathsteacher.com.au/year7/ch06_decimals/01_dec/Image8477.gif

Place value table from hundred thousandths to tens.

 

In expanded fractional form, 72.649 is written as:

http://www.mathsteacher.com.au/year7/ch06_decimals/01_dec/Image8479.gif

So, 72.649 has seven tens, two units, six tenths, four hundredths and nine thousandths.

 

We find from the place value table of 72.649 that:

·         The digit 6 is in the first place after the decimal point.  So, it represents:

http://www.mathsteacher.com.au/year7/ch06_decimals/01_dec/Image8480.gif
http://www.mathsteacher.com.au/year7/ch06_decimals/01_dec/Image8481.gif

·         The digit 4 is in the second place after the decimal point.  So, it represents:

http://www.mathsteacher.com.au/year7/ch06_decimals/01_dec/Image8482.gif
http://www.mathsteacher.com.au/year7/ch06_decimals/01_dec/Image8483.gif

·         The digit 9 is in the third place after the decimal point.  So, it represents:

http://www.mathsteacher.com.au/year7/ch06_decimals/01_dec/Image8484.gif
http://www.mathsteacher.com.au/year7/ch06_decimals/01_dec/Image8485.gif


In general:

To express the decimal place value of a number in fractional form, the position of the digit in the number tells us how many zeros are to be added after the 1 in the denominator.

 

For example, 3 in the decimal number 94.19547632 is in the 7th place after the decimal point.  So, it represents:

http://www.mathsteacher.com.au/year7/ch06_decimals/01_dec/Image8486.gif
http://www.mathsteacher.com.au/year7/ch06_decimals/01_dec/Image8487.gif


Example 1

Give the place value of 8 in the following decimal numbers:

a.  0.856
b.  0.384
c.
  0.4386
d.  0.16982

Solution:

http://www.mathsteacher.com.au/year7/ch06_decimals/01_dec/Image8488.gif

http://www.mathsteacher.com.au/year7/ch06_decimals/01_dec/Image8489.gif

http://www.mathsteacher.com.au/year7/ch06_decimals/01_dec/Image8490.gif

http://www.mathsteacher.com.au/year7/ch06_decimals/01_dec/Image8491.gif


Example 2

Write each of the following as a decimal number:

http://www.mathsteacher.com.au/year7/ch06_decimals/01_dec/Image8492.gif

Solution:

http://www.mathsteacher.com.au/year7/ch06_decimals/01_dec/Image8493.gif


Example 3

Write each of the following numbers in expanded fractional form:

http://www.mathsteacher.com.au/year7/ch06_decimals/01_dec/Image8494.gif

Solution:

http://www.mathsteacher.com.au/year7/ch06_decimals/01_dec/Image8495.gif


Example 4

Write each of the following decimal numbers in words:

http://www.mathsteacher.com.au/year7/ch06_decimals/01_dec/Image8496.gif

Solution:

a.  7.3 represents seven units and three tenths.
b.  84.6 represents eight tens, four units and six tenths.
c.  3.189 represents three units, one tenth, eight hundredths and nine thousandths.
d.  18.3478 represents one ten, eight units, three tenths, four hundredths, seven thousandths and eight ten-thousandths.
e.  0.008 represents eight thousandths.
f.   0.000 043 represents four hundred-thousandths and three millionths.

Convert decimals to fractions

http://www.mathsisfun.com/converting-decimals-fractions.html

Like and unlike decimals

http://www.hope.dek.cc/Like-unlike_decimals.htm

Ordering decimals

http://www.mathsisfun.com/ordering_decimals.html