# 5.12 * 2.0 = . Use correct amount of significant figures?

Mathprof, the answer is 10. (10 has potentially got 2 significant figures!)

There are only 2 significant figures in the 2.0 so you can only give answer to 2 sig figs.
10.24
it is equal to 10.240
actually it would be 10.2

2.0 is your limitation on significant figures.

math prof below has a good explanation

ACTUALLY - 10 has only ONE significant figure.. zeros on the end do NOT count as significant (only after the decimal do they count when on the end)
If you are using one significant figure, then the answer would be 10.
However, 5.12 has three sig fig and 2.0 has one.
One could conclude that the product should have three sig fig so the answer would be 10.2.

5.12 has 3 sig figs.
2.0 has 2 (not 1) sig figs.
Answer should be "10." (with the decimal point but no zero behind the decimal point)

Remember, the number of digits behind a decimal point always contribute to sig figs. The number of sig figs in an answer is determined by the number with the least number of sig figs in the original equation. The zero(s) in front of the decimal point don't count if the number is an integer, there is no decimal point, and the zero(s) are at the end of the number.
5.12 has 3 sig figs. 2.0 has 2 sig figs. The answer is 10.24 and since 2.0 has 2 sig figs, the answer is 10. I checked it on my TI-84 that has a sig fig calculator.
The answer would be 10. The rule for significant figures when multiplying and dividing is that you report the value to the least number of significant figures in the problem. 2.0 has 2 sig figs therefore th answer is 10.

10.24

2 sig figs --> has to be scientific notation to get 2 sig figs.

1.0 x 10^1
When a decimal point is present, all zeros between that decimal point and a digit are significant digits.
When a decimal point is not present, any zero not trapped between two nonzero digits are insignificant:
103 has 3 sf's
1030 has 3 sf's
1030. has 4 sf's
1030.00 has FIVE sf's
00010.0 has 3 sf's

Since your limiting value is 2.0, which hereby has TWO significant digits, the answer 10.24 must be rounded to have TWO significant digits.
10.24 raw has four significant digits
10.2 would be THREE significant digits
10. would be two significant digits.

To clear things up.. The answer is not just "10", but "10.".
It has to have a decimal point for that zero in the units' place to count.

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