Round 0.416666667 to 3 significant figures; Express 12000 in Standard form; Write 2.36 x 104 as a decimal number; How many significant figures are in 10.659 22.

To round to 3 significant figures:

1. Identify the first non-zero digit, which is 4.
2. Count three digits from the first non-zero digit: 4, 1, 6.
3. Look at the digit immediately after the third significant figure (which is 6). The digit is 6.
4. Since 6 is 5 or greater, round up the third significant figure (6 becomes 7).

$$0.416666667 \approx 0.417$$ $$\boxed{0.417}$$

Standard form is written as $a \times 10^n$, where $1 \le |a| < 10$ and $n$ is an integer.

1. Move the decimal point from the end of 12 000 to after the first non-zero digit (1). $$12000. \to 1.2000$$
2. Count the number of places the decimal point was moved. It was moved 4 places to the left.
3. So, $n = 4$.

$$12000 = 1.2 \times 10^4$$ $$\boxed{1.2 \times 10^4}$$

The exponent is 4, which means the decimal point moves 4 places to the right.

$$2.36 \times 10^4 = 2.3600 \times 10^4 = 23600$$ $$\boxed{23600}$$

Rules for significant figures:

• Non-zero digits are always significant.
• Zeros between non-zero digits are significant.
• Leading zeros (zeros before non-zero digits) are not significant.
• Trailing zeros (zeros at the end of the number) are significant only if the number contains a decimal point.

In the number 10.65922:

• 1 is a non-zero digit, so it's significant.
• 0 is between 1 and 6, so it's significant.
• 6, 5, 9, 2, 2 are non-zero digits, so they are significant. Counting all significant digits: 1, 0, 6, 5, 9, 2, 2. There are 7 significant figures.

$$\boxed{7}$$