Mathematics 7th

Question

If the number has been rounded, then should the trailing zeros be counted as significant? Say 8982 rounded to 9000, so what zero should be counted as significant and why? Please explain detailed if possible

Also When 8982 rounded to 2 significant figures, the answer is 9000. But according to the rule, if a number does not have a decimal, then don't count the zero after the last non-zero digit, which in this is 9. So according to me, 9000 only has 1 significant figure, but as for the question, it says round 8982 to two significant figures and the answer is 9000, and they include the first zero after 9 as significant. Can someone help?

Answer 1

8982

round once to get 8980, that last digit is the least reliable

round twice to get 9000.

that last 8 is least reliable, leaving 8(9+1)00 = 9000

IF you had started with 8882 and rounded once, you'd get 8880

round twice and get 8900.

Think of it another way.

say you had 0.8982 and rounded twice

first rounding would give 0.898, that last decimal such as when doing a measurement is least reliable so you round up or down. 2 is closer to 0 so you round down

then 2nd rounding is up. 8 >5, so you round up to get 0.8(next digit 9+1) That 9+1=10 carries over to the 8 as 8+1= 9, leaving 0.9000

for integers, not fractional numbers, you get the same result 9000 as the twice rounded number of 8982

but with 8982 that 2nd rounding can only result in 9000

But maybe someone else can explain it better. Reliability in measurements is one way to go.