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.