Note about multiplying by tens, hundreds, tenths and hundredths etc
Look at these examples and try to work out a rule for multiplying by powers
of ten.
d.p. means decimal place, i.e. the number of digits to the right of a decimal point
when I write zero, I really mean power of ten, but I think you will see what I mean
Note that 3 x 2 = 6,
and
and
3 x 20 = 60
one zero in the problem, one zero in the answer
30 x 2 = 60
one zero in the problem, one zero in the answer
30 x 20 = 600
two zeroes in the problem, two zeroes in the answer
3 x 200 = 600
two zeroes in the problem, two zeroes in the answer
300 x 2 = 600
two zeroes in the problem, two zeroes in the answer
0∙3 x 2 = 1∙2
one d.p. in the problem, one d.p. in the answer
3 x 0∙2 = 1∙2
one d.p. in the problem, one d.p. in the answer
0∙3 x 0∙2 = 0∙6
two d.p.s in the problem, two d.p.s in the answer
3 x 0∙02 = 0∙6
two d.p.s in the problem, two d.p.s in the answer
0∙03 x 2 = 0∙6
two d.p.s in the problem, two d.p.s in the answer
Tens and hundreds cancel out tenths and hundredths,
0.3 x 20 = 6
one dp cancels out one zero
30 x 0∙2 = 6
one dp cancels out one zero
0.3 x 200 = 60
one dp cancels out one zero, there is still one zero left
300 x 0.2 = 60
one dp cancels out one zero, there is still one zero left
300 x 0.02 = 6
two dps cancels out two zeroes