To solve the problem of multiplying [tex]\( 24.32 \)[/tex] by [tex]\( 0.010 \)[/tex] and then rounding the result to two significant figures, we can follow these steps:
1. Identify the numbers involved:
- The first number is [tex]\( 24.32 \)[/tex].
- The second number is [tex]\( 0.010 \)[/tex].
2. Perform the multiplication:
- Multiply [tex]\( 24.32 \)[/tex] by [tex]\( 0.010 \)[/tex]:
[tex]\[
24.32 \times 0.010 = 0.2432
\][/tex]
3. Round the result to two significant figures:
- The number [tex]\( 0.2432 \)[/tex] needs to be rounded to two significant figures.
- The first significant figure is [tex]\( 2 \)[/tex] (the first non-zero digit in the result).
- The second significant figure is [tex]\( 4 \)[/tex] (the digit after [tex]\( 2 \)[/tex]).
Rounding [tex]\( 0.2432 \)[/tex] to two significant figures involves looking at the third digit, which is [tex]\( 3 \)[/tex]. Since [tex]\( 3 \)[/tex] is less than [tex]\( 5 \)[/tex], we do not need to round up:
[tex]\[
0.2432 \approx 0.24
\][/tex]
Thus, [tex]\( 24.32 \times 0.010 = 0.2432 \)[/tex], and rounded to two significant figures, the result is [tex]\( 0.24 \)[/tex].
Therefore, the answer is:
[tex]\[
0.24
\][/tex]
