Question

how can we write 5.1 to exactly six significant figures? *
both of these are correct
5.10,000x10^0
neither of these is correct
5.10,000
how can we write 70,000 to exactly two significant figures? *
7.00x10^4
none of these is correct
7.0x10^4
70,000

Explanation:

Step1: Recall significant - figures rules

Significant figures include all non - zero digits and zeros between non - zero digits. In scientific notation, all digits in the coefficient are significant.

Step2: Analyze writing 5.1 to six significant figures

The number 5.1 has two significant figures. To write it with six significant figures in scientific notation, we can write it as $5.10000\times10^{0}$. In standard form, it can also be written as 5.10000. So both $5.10000\times10^{0}$ and 5.10000 are correct ways to write 5.1 with six significant figures.

Step3: Analyze writing 70000 to two significant figures

The number 70000 has one significant figure in its current form. In scientific notation, to have two significant figures, we write it as $7.0\times 10^{4}$. The number $7.00\times10^{4}$ has three significant figures, and 70000 has one significant figure.

Answer:

1. Both of these are correct
2. $7.0\times10^{4}$