To solve the problem of finding [tex]\(0.734 \times 0.029\)[/tex] correct to 3 significant figures, follow these steps:
1. Perform the Multiplication:
First, multiply the two given numbers:
[tex]\[
0.734 \times 0.029 = 0.021286
\][/tex]
2. Check the Result and Identify Significant Figures:
The raw result of the multiplication is [tex]\(0.021286\)[/tex]. This number has more than three significant figures, so we need to round it.
3. Round to 3 Significant Figures:
To round [tex]\(0.021286\)[/tex] to three significant figures, look at the fourth figure to decide whether to round up or down. The first three figures are 0.021 (2, 1, and 2 from 0.0212). The fourth figure, which is the place we look at for rounding, is 8.
Since the digit after the third significant figure is 8 (which is 5 or higher), we round up.
[tex]\[
0.021286 \approx 0.0213
\][/tex]
However, since we are only required to report three significant figures, we omit the last digit, keeping only the first three figures significant:
[tex]\[
0.021286 \approx 0.021
\][/tex]
4. Final Answer:
Therefore, [tex]\(0.734 \times 0.029\)[/tex], when rounded to three significant figures, is:
[tex]\[
0.021
\][/tex]
