Why does 5.2 x0.1 =0.52 and why does 5.2 divided by 0.1 = 52.?

5.2 = 52/10 and 0.1 = 1/10
so = 52/10 × 1/10
= 52 /100 = 0.52
and
52/10 ÷ 1/10 ----------division is inverse of multiplication
= 52/10 × 10/1
= 52

An easy way to tackle 5.2 x 0.1 = 0.52 would be;

forget the decimal points and you have, 52 x 1 = 52
then look and count how many digits are after the decimal point, in this case it is 2 ( the .2 and the .1)

then move the decimal point 2 places to the left

i.e 52 becomes after one decimal point to left 5.2
after the second decimal point to the left 0.52


The second questions of yours can be done by;

multiply both 5.2 and 0.1 by 10 and you get 52 and 1
so therefore 52 divided by 1 = 52

Hope this helps..

hi!

if u multiply a number by 0.1 move the decimal point of the number one place to the left.

if u divide a number by 0.1 move the decimal point of the number one place to the right.

the answer in division is larger than the answer in multiplication because... analyze this...
0.1 is a number less than 1
we know that if u multiply a number by 1, the answer is that number.
but since 0.1 is far lower than 1, of course when a number is multiplied to 0.1, the answer is smaller.

if u divide a number by 1, the answer is that number. if you divide it by two, the quotient is smaller
so, we'll realize that if that number is divided by a smaller number, it will have a larger quotient.

i hope this helps

=)

Brillaint question i could upload :P ''The broomstick spun to earth,yet he purely controlled to snatch the strap of his rucksack and the best of the owls cage as he clung to the sting of the bike.'' Harry Potter and The Deathly Hallows

5.2x0.1=0.52 because 0.1 actually equals 1/10therefore 5.2is divided by 10, which makes it (0.52), while 5.2 divided by 0.1 is equal to the following 5.2 divided by 1/10 which equals to 5.2x10/1 =52

in your sum "5.2 x 0.1", it looks like theres no division going on, whereas in your other sum, we can all see there clearly is some division going on. well...i have news. there is division going on in both sums, just in the first, it's hidden from view.

i'll show you where it is.

0.1 is the number 1 DIVIDED by 10

so...5.2 x 0.1 is the same as
5.2 x 1 divided by 10


to make that last sum i gave clearer, we can solve that "5.2 x 1" bit of it (here you go: 5.2 x1 = 5.2) so we're left with just

5.2 divided by 10

in other words, we've show that 5.2 x 0.1 is the same as 5.2 divided by 10.

5.2 divided by 10 is 0.52 - see, the dividing was in the first sum you gave all along, just it was hidden inside the number "0.1"

Hi!~

First, I suggest you change them into fractions. Then you'll understand.

5.2 x 0.1 = 0.52
because
You're sharing 5.2 parts equally among 1/10th of a person (which isn't possible, but anyways).

In other words, usually when you multiply by a whole number, you're multiplying by a factor.

But when there are two people you don't have enough of one portion, so you have to buy two portion of 1 to get the right quantity.

With less than one person, it's hard to grasp this concept simply because this is impossible in real life! This is like giving an arm the one portion. That arm won't need that entire portion of whatever, so you're really sharing it equally by assuming there are ten arms and you divide that equally among all then arms, then taking one portion of the ten arms to that one arm.

In other words (again), by multiplying any number, you're making it so that it complies with the amount for that number of people listed. And since it's 0.1, you don't need more than one person.

Thus 5.2 x 0.1 = 0.52 (multiplying by a scale factor smaller than one)

For 5.2 divided by 0.1 = 52, it's the same.

Think about it. For numbers > or equal to 1, you're dividing that portion equally of that number.

5.2 divided by 2
can be explained by words as
5.2 portions of whatever you have divided equally into 2 portions

5.2 divided by 1
can be explained by words as
5.2 portions of whatever you have divided equally into 1 portion

5.2 divided by 1/2
can be explained by words as
5.2 portions of whatever you have divided equally into 1/2 half part

In other words, one 1/2 is 5.2, thus adding 5.2 satisfies the quantifier in the question.

the difference between numbers above or equal to one, or numbers below one,

1. numbers above or equal to one = you are splitting the existent into equal parts, whereas,

2. numbers below or equal to one = you are fulfilling whatever is left of the already split whole part (the original part), thus the number gets bigger.

Hope this helps!

5.2 x 0.1
= 5.2 x 1/10
= 5.2/10
= 0.52

5.2 ÷ 0.1
= 5.2 ÷ 1/10
= 5.2 x 10/1
= 52/1
= 52

becuase you are timesing by 0.1 so the number will shift down 1 decimal place and its pretty much the same with the dividing thing

5.2 x 0.1 = 5.2 x 1/10 = 5.2/10 = 0.52

5.2 / 0.1 = 5.2 / 1/10 = 10 x 5.2 = 52