Why does .3000=.3 or .120000=.12 ? I just cant get the mental picture, can some one plz explain it in detail.?

Question

Math

Answer 1

What does 0.3000 actually mean? In the number system we use, it means

Zero units
3 Tenths
0 Hundredths
0 Thousandths
0 Ten-Hundreths

The size of the number can be imagined as adding together all these peices. So 0.3000 is

zero units + 3 tenths + 0 Hundredths... etc

However, adding zero to something doesn't change the sum? a+0=a for any number a you pick. So the extra zeroes are not needed, and we just drop them.

Equivalently, 000013 is the same as 13. Because we are adding 3 units, 1 ten, zero hundreds, 0 thousands. Since adding zero doesn't change anything we omit these leading zeroes. This is a familiar idea, seeing 00013 written down looks stupid, and thats the real reason why. Its the same concept with decimals.

Answer 2

All those 0s are confusing you because in numbers without a decimal point 0s on the end make the number bigger. They way they do this is by forcing the important digits of the number -- the ones that aren't 0 -- to the left. And every time you move a digit to the left it means 10 x more than it did before.

Now, when you've got a decimal point there, adding 0s on the end doesn't move anything to the left. The decimal point acts like a kind of barrier that digits can't cross. So adding more 0s does absolutely nothing, and 0.3000 is exactly the same number as 0.3. The only reason you might want to add the 0s is to make it clear that you know that the number is exactly 0.3 and not, say, 0.3001, which is a tiny bit bigger.

By the way, you should always put a 0 before the decimal point, because if you photocopy .3000 a few times it can easily turn into 3000!

Hope that helps.

Answer 3

Try this:
0.120000 = 1/10 + 2/100 + 0/1000 + 0/10000 + . . .
You can erase all the fractions with 0 numerator, leaving
0.120000 = 1/10 + 2/100 = 0.12
You can add as many 0's as you please after the decimal portion of a number, and its value will be unchanged. By the same token, if there is no other number in that string of 0's you can erase them all.

Answer 4

zeroes only change the value of a number when they are used as placeholders, i.e. to distance a digit from the decimal point (on either side) - "30" is not the same as "3" because in "30" the digit 3 is in the tens' place, meaning that there are 3 groups of ten. The zero is used to show that there is nothing in the ones' place.

don't feel bad; it took the ancients many hundreds of years to understand the zero.

Answer 5

0.3000 = 3000/10000 = 3/10 = 0.3

0.120000 = 120000/1000000 = 12/100 = 0.12

Hope that helps!

Answer 6

As the zeros after point describes fractions:

3 / 10 = 0.3

30 / 100 = 0.30

300 / 1000 = 0.300

3000 / 10000 = 0.3000

30000 / 100000 = 0.300000

these are all equal

Answer 7

.3 is equal to .3000 since .3000 does not have avalue after 3 .
meaning in .3 the zeroes that followes are ignored as insignificant.

Answer 8

the zeros are meaningless in this case. If it was .300002, then the zeros are fine. But the zeros for .3000 don't need to be there.

Just like:

12.0
1567.00000000
0.100000000

On those you can rid yourself on the zeros. You can attach as many zeros as you want to .3, but its still the same thing as .3. I know that didn't really help..........

Answer 9

0.3000 isn't really equal to 0.3

0.3000 says that the number has been written correct to 4 decimal places. In other words any number in the range

0.29995 < 0.3000 ≤ 0.30005

will correct to 0.3000

Whereas 0.3 is written correct to 1 dp (unless it is exact! and you can't tell without more information.)
and so any number in the range

0.25 < 0.3 ≤ 0.35

will correct to 0.3.

Answer 10

Those zeros at the right are insignificant figures.