# Significant figures with multiplication

1. May 27, 2013

### ikihi

1. The problem statement, all variables and given/known data

what is 33.3 X 45.1 using significant figures?

2. Relevant equations

basic multiplication and significant figures.

3. The attempt at a solution

I got 1501.83 in my calculator. I'm confused with the original problem because it has 4 digits before the period however you have to round the answer to 3 significant figures. (It isn't asking for scientific notation)

is it any of these: ≈1501 or ≈1502 or ≈1500?

Last edited: May 27, 2013
2. May 27, 2013

### Simon Bridge

note $0.33\times 10^2 = 3.33\times 10^1 =33.3 = 333 \times 10^{-1}$ all have 3 sig fig.
so... $1502=1.502\times 10^3$ how many sig fig?

3. May 27, 2013

### ikihi

1.502X10^3 has 4 significant figures.

Hmm I thought 0.33 X 10^2 has only 2. Why does it have 3 significant figures?

Anyway I'm confused with the original problem because it has 4 digits before the period (1501.) however you have to round the answer to 3 significant figures. Its not asking for scientific notation.

Last edited: May 27, 2013
4. May 27, 2013

### Simon Bridge

Argh - because it's a typo.

But putting things in scientific notation can be a way to check you have the right sig fig.

Scientifically, 3.33 and 3.30 have the same sig fig ... but you cannot tell of 330 is 2 or 3 sig fig.
(a measurement of 3.3 units is different from a measurement of 3.30 units)

Your problem is that you cannot see if "1500" is 2, 3 or 4 sig fig.
But if you wrote 1.50x103 it would be clearer right?

Also - consider 0.02 ... how many sig fig? That's 2x10-2 ... that help?
What if it was the result of 66/3300 ?

The bottom line is that the sig-fig approach is not all that useful.
You will stop using it when you leave secondary school.

The correct way to write that result is: 1500 units (3 sig-fig)

5. May 28, 2013

### ikihi

i see. thankyou