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You are HERE >> Mathematics  > Grade 5

Comparing Decimals
By Lisa Williams
January 27, 2002


Comparing decimals: How to figure out which is greater:

One book I have says that when comparing decimals with different names, change them to decimals having the same name. To state this in Mississippian English, make sure all the decimals have the same amount of numbers after (or to the right of) the decimal point. You do this by adding zero's to the end of the decimals if necessary. Look to the examples below. Another thing I find helpful is to either say the names of the decimals or write out their names as I have in the examples. 

It makes no sense at all to me if I called these decimals:

0.09 zero point zero nine
0.17 point seventeen
0.052 zero point zero five two
0.076 zero point zero seven six

Instead be sure to use their place value names

0.09 is nine-hundredths 
0.17 is seventeen hundredths 
0.052 is 52 thousandths 
0.076 is 76 thousandths

Add zero's to make all the decimals have the same place value name. In Mississippian English you are changing them all to thousandths since that is the lowest place value of the decimals given. All of them now have 3 numbers after the decimal point.

0.09 becomes 0.090 or 90 thousandths 
0.17 becomes 0.170 or 170 thousandths

SO you have 

0.09 becomes 0.090 or 90 thousandths 
0.17 becomes 0.170 or 170 thousandths 
0.052 is 52 thousandths 
0.076 is 76 thousandths

Now you can plainly see which is least and which is greatest. 
The least is 0.052, then 0.076, 0.09 with the greatest being 0.17 the greatest. 

If I added more than one zero to 0.09 making it 0.0900 then this decimal would read 900 ten-thousandths because the last zero was in the 10,000th's place. You could keep going and add still more zero's 0.090000 making this read 90,000 millionths.

Let's practice:
Change the following decimals to thousandths
1.) 0.3     2.) 0.56   3.) 0.04    4.) 0.7  5.) 0.9400

Compare these decimals to find the larger one. Remember that the decimal must have the same amount of numbers after the decimal point, thereby having the same place value name BEFORE you can compare them correctly.

Which is larger?
6.) 0.5  or 0.51
add a zero to 0.5 (5 tenths) to make it 0.50 (50 hundredths)

Now you can either say which is greater 0.50 (50 hundredths) or 0.51 (51 hundredths) by saying their names to yourself or you can line up the decimals and tell at a glance which is greater.
0.50
0.51 obviously 0.51 is bigger.

I personally prefer the lining them up and adding zero's method but my oldest daughter used both till she got it figured out.

7.) 0.453 or 0.4506      8.) 1.16 or 1.6      9.) 0.29 or 0.229       10.) 3.5 or 3.49

11.) Write in order from smallest to largest:
  0.025      0.67         1.32       0.25     0.829      1.67

a._______   b._______   c.________ d.________ e. ________ f.__________
 
 

Answers:
(Note all the following decimals now have the same number of digits after the decimal point. it is now a simple matter to see which is larger than the other)
1.) 0.300   300 thousandths
2.) 0.560   560 thousandths
3.) 0.040     40 thousandths
4.) 0.700   700 thousandths
5.) 0.940   940 thousandths

7.) 0.453 or 0.4506 
0.4530 four-thousand five-hundred thirty ten-thousandths 
0.4506 four-thousand five-hundred six ten-thousandths 

0.453 is bigger

8.) 1.16 or 1.6 
  1.60  one and 60 one-hundredths
  1.16  one and 16 one-hundredths 

1.6 is bigger

  9.) 0.29 or 0.229
      0.290    290 thousandths
      0.229    229 thousandths

0.29 is bigger

 10.) 3.5 or 3.49
        3.50  three and 50 one-hundredths
        3.49  three and 49 one-hundredths

         3.5 is bigger

11.    Line up your decimal places first
         0.025        25 thousandths
         0.67          67 hundredths
         1.32          1 and 32 hundredths
         0.25          25 hundredths
         0.829        829 thousandths
         1.67          1 and 67 hundredths

 Your smallest decimal place is thousandths so you change them all to thousandths.
         0.025        25 thousandths
         0.670          670 thousandths
         1.320          1 and 320 thousandths
         0.250          250 thousandths
         0.829        829 thousandths
         1.670          1 and 67 thousandths

Now you can see that they go in this order:

a) 0.025   b) 0.25   c) 0.67   d) 0.829   e) 1.32   f) 1.67

 


 
Submitted by: Copyright© Lisa Williams I'm a homeschooling mom of 3 elementary school age children. I run a clowning business from my home (Jingles the clown), am pianist for a local church, teach a Sunday School class, teach piano, tutor basic math see Math tutoring and algebra online and I enjoy making people smile. Send a note to Lisa

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