Write 0.416666667 correct to 3 significant figures.

Here are the solutions to the questions:

8. Write 0.416 666 667 correct to 3 significant figures.

Working out:
To round to 3 significant figures, we identify the first non-zero digit, which is 4.
The first three significant figures are 4, 1, and 6.
The digit immediately following the third significant figure (6) is 6.
Since 6 is 5 or greater, we round up the third significant figure.
So, 6 becomes 7.

Answer:

$$\boxed{0.417}$$

9. Express 12 000 in Standard form.

Working out:
Standard form is written as $a \times 10^n$, where $1 \le |a| < 10$ and $n$ is an integer.
For $12 000$, we need to move the decimal point from its implied position after the last zero to between the 1 and the 2.
The decimal point moves 4 places to the left.
So, $a = 1.2$ and $n = 4$.

Answer:

$$\boxed{1.2 \times 10^4}$$

10. Write $2.36 \times 10^3$ as a decimal number (ordinary form).

Working out:
The exponent is 3, which means we move the decimal point 3 places to the right.
Starting with 2.36, moving the decimal 3 places to the right gives:
$2.36 \rightarrow 23.6 \rightarrow 236. \rightarrow 2360.$

Answer:

$$\boxed{2360}$$

11. How many significant figures are in 10.659 22

Working out:
We count the significant figures based on the rules:

• Non-zero digits are always significant. (1, 6, 5, 9, 2, 2 are significant)
• Zeros between non-zero digits are significant. (The 0 between 1 and 6 is significant) So, all digits in 10.65922 are significant.

Answer:

$$\boxed{7}$$