3 Significant zeros

Deciding whether zeros are significant is difficult because zeros can be used for counting OR they can be used as labels When are zeros used for counting? When are zeros not significant? When are zeros used as labels? When are zeros significant? When they are used as labels One example is money, such as counting “10” hundred dollar bills. When they are used for counting One example is money, such as the two zeros on “ hundred dollar bills. Story Time

5 $100 bills 50 $10 bills 500 $1 bills $400 to $600 $490 to $510 Suppose that you take your car to a mechanic, and he says the repair will cost about 500 $1 bills Suppose that you take your car to a mechanic, and he says the repair will cost about 50 $10 bills Suppose that you take your car to a mechanic, and he says the repair will cost about 5 $100 bills Suppose that after the repair is completed the mechanic charges you 52 $10 bills? It that acceptable? Suppose that after the repair is completed the mechanic charges you 51 $10 bills? It that acceptable? Suppose that after the repair is completed the mechanic charges you 49 $10 bills? It that acceptable? How much money do you expect to spend? Suppose that after the repair is completed the mechanic charges you 499 $1 bills? It that acceptable? Suppose that after the repair is completed the mechanic charges you 502 $1 bills? It that acceptable? Suppose that after the repair is completed the mechanic charges you 501 $1 bills? It that acceptable? Suppose that after the repair is completed the mechanic charges you 4 $100 bills? It that acceptable? Suppose that after the repair is completed the mechanic charges you 7 $100 bills? It that acceptable? Suppose that after the repair is completed the mechanic charges you 6 $100 bills? It that acceptable? Yes. The estimate was about 50 $10 bills, so it can be one bill more Yes. The estimate was about 5 $100 bills, so it can be one bill less No. The estimate was about 50 $10 bills, so it can not be two bills more Yes. The estimate was about 5 $100 bills, so it can be one bill more Yes. The estimate was about 500 $1 bills, so it can be one bill more Yes. The estimate was about 500 $1 bills, so it can be one bill less Yes. The estimate was about 50 $10 bills, so it can be one bill less No. The estimate was about 500 $1 bills, so it can not be two bills more No. The estimate was about 5 $100 bills, so it can not be two bills more You expect to spend about $500 – five hundred dollars 5 $100 bills 50 $10 bills 500 $1 bills $400 to $600 $490 to $510 $499 to $501 Both zeros are labels So, one sig. fig. One zero is a label The other is for counting So, two sig. fig. Neither zero is a label Both zeros are for counting So, three sig. fig.

Now, how many significant figures in each number? Here are some examples Significant Zeros Not significant Zeros 10001 1000. 1000.00 .00015 1000 Now, how many significant figures in each number? Are these Zeros Sig. or not Sig. 1203 Sig. 4 5460. Sig. 4 1200 Not Sig. 2 .00546 Not Sig. 3 1200. Sig. 5460 Not Sig. 3 4 5 .1203 Sig. 4 50406 Sig. .1230 Sig. 4 54600.00 Sig. 7 .0123 Not Sig. 3 54600. Sig. 5

Now, how many significant figures in each number? Here are some examples Here are some examples Significant Zeros Not significant Zeros 10001 1000. 1000.00 .00015 1000 Now, how many significant figures in each number? 12030 4 54060 4 1230 3 540.60 5 .0540 3 .001203 4 .005600 4 12.30 4 .05060 4 123.00 5 0.0056 2 5 .12030