   SEARCH HOME Math Central Quandaries & Queries  Question from alwyn, a parent: Dear all there please help me, Why should when you Multiplying Decimal numbers is value becoming less and less? don't you think even decimal number is a quantity and in no chance when it multiplies its should become less or nil !!! In fact all multiplying and or adding the value will go up and only when you subtract and divide it should become less !! waiting Alwyn We have two responses for you

Hi Alwyn,

It is an easy to believe what you say is true especially if you think of multiplication as repeated addition. For example 3 × 5 = 5 + 5 + 5 = 15. But multiplication is more than repeated addition. For example

one half of 12 is 6

or said in an equation

1/2 × 12 = 6

or in decimal form

0.5 × 12 = 6.

If d is a number less than 1 then a × d is less than a. It is a fractional part of a, the fraction being d.

I hope this helps,
Penny

Hi Alwyn.

Let's pretend that I am a lump of radioactive waste. Because I am
radioactive, I decay over time. That means (in my case; I'm making up
the numbers here) that in 1 year, only 97% of my will still be here.
Each year, I lose 3% of my mass.

Percentages are the same as decimals: 0.97 = 97%. So let's say today
I am 1000 grams. In one year, I will be 970 grams (0.97 x 1000 =
970). In two years, I will by 0.97 x 970 = 940.9 grams. Continue
this: in 10 years, I will be about 737 grams and in 100 years I will
be about 48 grams...never disappearing entirely, but certainly getting
smaller.

So 1000 x 0.97 is bigger
than 1000 x 0.97 x 0.97, which in turn is bigger
than 1000 x 0.97 x 0.97 x 0.97, which in turn is bigger
than 1000 x 0.97 x 0.97 x 0.97 x 0.97, which in turn is bigger
than 1000 x 0.97 x 0.97 x 0.97 x 0.97 x 0.97, etc.

For another example, let's say I win the lottery: $1,000,000. I decide that each week, I will spend half (0.5 times) what I have left. Week 1 I spend 0.5 x 1,000,000 =$500,000. I buy a mansion.
Week 2 I spend 0.5 x 500,000 = $250,000. I set up a scholarship fund for budding student mathematicians. Week 3 I spend 0.5 x$250,000 = $125,000 on a yacht. Week 4 I spend 0.5 x$125,000 = $62,500 supplying a village in a poor country with school supplies and a teacher. Week 5 I spend 0.5 x$62,500 = \$31,250 on a round-the-world cruise for
my parents.
and so on.

Each time, the amount gets smaller and smaller.

Hope these examples help explain things.
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.