Question

How many significant figures can the final answer have? `(29 - 20.2) xx 1.79 xx 10^2 -: 1.37`

Answer 1

The final answer can have only one significant figure.

Explanation:

Remember PEMDAS

This means that you do what is possible within

`color(red)(bb"p"`arentheses first, then
`color(red)(bb"e"`xponents, then
`color(red)(bb"m"`ultiplication and `color(red)(bb"d"`ivision (from left to right), and then
`color(red)(bb"a"`ddition and `color(red)(bb"s"`ubtraction (from left to right).

We first evaluate the term in parentheses: (29 -20.2).

For this. we use the rules for subtraction:

• Count the number of significant figures in the decimal portion of each number.
• Subtract as usual.
• Round the answer to the FEWEST number of places in the decimal portion of any number.

In this problem, we have

There is no number to the right of the implied decimal place in 29, so the answer can have no number to the right of the decimal place.

This number can have only one significant figure.

If we must record this number, we write it as 9.

If we use it in other operations, we keep it as 8.8 in our calculator and round off at the end.

The other operations are multiplication and division.

We keep the number 8.8 in our calculator and do the operation

`8.8 × (1.79 × 10^2)/1.37 = 1149.781022`

However, the answer can have only one significant figure.

We round it off and write the answer as `1 × 10^3`.