Question

How do you round each number to four significant figures? 0.004384010 cm and 431,801 kg?

Answer 1

`0.00color(red)(1384)` cm and `color(blue)(431,8)00`kg

Explanation:

Start counting significant figures from the first non-zero digit from the left.

`0.00color(red)(1384010)`cm has 7 significant figures.

`0.00color(red)(1384)` cm has 4 significant figures. (the others fall away)

`color(blue)(431.801)` kg has 6 significant figures. the size of the number is about four hundred thousand. Despite any rounding, it must still be about four hundred thousand

`color(blue)(431,8)00` kg has 4 significant figures. (the others fall away and are replaced by 0's as place holders.)

Answer 2

The answers are 0.004 384 cm and 431 800 kg.

Explanation:

Here are the four rules you need.

1. All `color (red)("non-zero digits")` are significant.
2. `color(red)"Inside zeroes"` (zeroes between significant digits) are significant.
3. `color(red)("Trailing zeroes in the decimal portion")` of a number are significant.
4. If the first digit to be dropped is `color(red)("less than 5")`, drop it and all the digits to the right of it.

0.004 384 010 cm

The three leading zeroes are not significant, but the inside zero and the trailing zero are significant.

There are 7 significant figures.

The first 4 significant figures are 4384, so the first digit to be dropped is 0.

We therefore drop it and all the following digits.

To 4 significant figures, `"0.004 384 010 cm = 0.004 384 cm"`.

431 801 kg

I am assuming that your comma is a thousands separator.

The inside zero is significant, so there are 6 significant figures.

The first 4 significant figures are 4318, so the first digit to be dropped is 0.

We therefore drop it and the following 1 and replace them with zeroes.

To 4 significant figures, `"431 801 kg = 431 800 kg "`.