Zeros in Decimals
Did you get some surprising answers from the 10% calculators? You may have been expecting an answer like 0.30 and gotten an answer like 0.3. What is the difference between these two numbers????
Before trying to figure that out, you may want to watch this video which explains some things about how decimals work:
Before trying to figure that out, you may want to watch this video which explains some things about how decimals work:
Now that you know something about decimal place value, think again about those two numbers.
The number 0.3 means zero ones and three tenths. That's like zero whole apples and three big slices (tenths) in the video.
The number 0.30 means zero ones, three tenths, and zero hundredths. That's like zero whole apples, three big slices, and zero tiny little slices (hundredths).
Here are pictures of those numbers:
The number 0.3 means zero ones and three tenths. That's like zero whole apples and three big slices (tenths) in the video.
The number 0.30 means zero ones, three tenths, and zero hundredths. That's like zero whole apples, three big slices, and zero tiny little slices (hundredths).
Here are pictures of those numbers:
The zero at the end of 0.30 doesn't change how many pieces of apple you have. Whether you write 0.3 or 0.30, you still have the same three slices of apple. The two numbers mean the same thing! When you have zeros at the very end of a decimal number, they tell you that you don't have any pieces of that size, so you can show the same number by writing it without the zeros at the end.
Here are a few more examples:
5.400 means the same thing as 5.40 and 5.4
0.803 means the same thing as 0.8030 and 0.80300000
$6.70 means the same thing as $6.7, but with money we almost always do write the zero at the end.
But watch out... if there are any numbers after the zeros, then you do need them!
0.50001 does not mean the same thing as 0.51!
[One other little thing - those extra zeros at the end can be important to scientists. In some science applications, it matters whether you have zeros on the end or not, but most of the time it doesn't matter. If you want to learn more about this, here is a page that explains it a little bit... but you don't need to read this to continue with the percents lessons!]
Here are a few more examples:
5.400 means the same thing as 5.40 and 5.4
0.803 means the same thing as 0.8030 and 0.80300000
$6.70 means the same thing as $6.7, but with money we almost always do write the zero at the end.
But watch out... if there are any numbers after the zeros, then you do need them!
0.50001 does not mean the same thing as 0.51!
[One other little thing - those extra zeros at the end can be important to scientists. In some science applications, it matters whether you have zeros on the end or not, but most of the time it doesn't matter. If you want to learn more about this, here is a page that explains it a little bit... but you don't need to read this to continue with the percents lessons!]