Now, you may ask "How many places should I move the decimal?"
The answer depends on which power of ten you are using

For 10 (=10¹) we will be moving the decimal by one place ;
For 100 (=10²) we will be moving the decimal by two places ;
For 1,000 (=10³) we will be moving the decimal by three places ;
For 10,000 (=10⁴) we will be moving the decimal by four places ;
How many places do you think we would have to move the decimal for 100,000 and 1,000,000?

Let's look at some numbers to see this in action

1.3 * 100
First think of 1.3 as 1.300
Now we are multiplying by 100, so we move the decimal two places to the right
1.300 * 100 = 130.0 = 130

Now let's do the same problem as division
1.3/100
First of all think of 1.3 as 001.3
Now we are dividing by 100, so we move the decimal two places to the left
1.3/100 = 001.3/100 = 0.013

One more set of problems: This time we're going to multiply and divide 5 by 10000.

First of all for 10000 we will be moving the decimal four places either to the right (multiplication) or the left (division).

Multiplication
5 * 10,000 = 5.00000 * 10,000 = 50000.0 = 50000 = 50,000

Division
5/10,000 = 00005./10,000 = 0.0005

Remember a < b means a is less than b ; a > b means a is greater than b

Let's examine 0.63 and 0.45
Now .63 is 6/10 + 3/100.
.45 is 4/10 + 5/100
Now since 6/10 is obviously larger than 4/10 we can conclude that .63 > .45 (.65 is greater than .45)

In this next example we'll see what happens when the first digit is the same

Your numbers are .67 and .69
.67=6/10 + 7/100
.69=6/10 + 9/100
Now the first digit is the same in both cases, so go on to the next digit
6/10 = 6/10 and 7/100 < 9/100 so we can conclude
.67 < .69 (.67 is less than .69)

One last example, but this one will be a little tricky

.5 and .43
Now it may look like comparing the numbers "five" and "forty-three", but that is not the case
It is really comparing "five tenths" and "forty-three hundredths"
.5=5/10
.43=4/10 + 3/100
Since 5/10 > 4/10, we can conclude .5 > .43

[Note: It may help you visulize this if you add a zero to the .5 making it .50]

In rounding off you decide how many decimal spaces you want and look at the number just beyond it.

• If that digit is 0, 1, 2, 3, or 4 then just cut the number off where you want to and be done with it. This is known as rounding down
• If that digit is 5, 6, 7, 8, or 9 then increase the digit at the cut off point by one. This is known as rounding up.

So with the $1.39 item, we want to round off to a whole number.
Look at the first decimal: 3. 3 < 5 so we can just cut the number off at 1.

1.39 is rounded off at 1

Now with 6.346 we wanted to round off to two places (or to the nearest hundredth).
Look at the third decimal: 6.
6 > 5 so we round up

6.34 is rounded up to 6.35

How about if we wanted to round off 5.79767 to the nearest hundredth (i.e. 2 decimal places)
Looking at the third digit 7 we decide we have to round up.

Thus 5.79767 is rounded up to 5.80 (in order to increase the 9 by one, we end up increasing the 79 to 80)

One last example, then your own your own

Round off 3.4451 to the nearest thousandth (i.e. 3 decimal places).
Well we look to the fourth digit: 1 and decide to round down.
Just cut off the decimal where we want it

3.4451 is rounded off to 3.445