Here are the solutions to the next set of problems: 8. Write 0.416 666 667 correct to 3 significant figures…

Question

Here are the solutions to the next set of problems: 8. Write 0.416 666 667 correct to 3 significant figures. 9. Express 12 000 in Standard form. 10. Write 2.36 × 10⁻³ as a decimal number.

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here are the solutions to the next set of problems:

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

Identify the first three significant figures.
The first non-zero digit is 4, so it is the first significant figure. The first three significant figures are 4, 1, and 6.
Look at the fourth significant figure to determine rounding.
The fourth significant figure is 6.
Round the third significant figure.
Since the fourth significant figure (6) is 5 or greater, round up the third significant figure (6) by adding 1 to it.
$0.416 \rightarrow 0.417$
Answer:
Correct to 3 significant figures, the number is $\boxed{\mathbf{0.417}}$ .

9. Express 12 000 in Standard form.
Place the decimal point after the first non-zero digit to get a number between 1 and 10.
For 12 000, the decimal point is implicitly at the end (12000.). Moving it to get 1.2.
Count how many places the decimal point was moved.
The decimal point moved 4 places to the left (from after the last 0 to between 1 and 2).
Write the number in standard form $a \times 10^n$ .
Since the original number is greater than 1, the exponent $n$ is positive.
$1.2 \times 10^4$
Answer:
12 000 in standard form is $\boxed{\mathbf{1.2 \times 10^4}}$ .

10. Write $2.36 \times 10^{-3}$ as a decimal number (ordinary form).
Identify the exponent of 10.
The exponent is -3. This means the decimal point needs to be moved 3 places to the left.
Move the decimal point.
Starting with 2.36, move the decimal point 3 places to the left, adding zeros as placeholders.
$2.36 \rightarrow 0.236 \rightarrow 0.0236 \rightarrow 0.00236$
Answer:
$2.36 \times 10^{-3}$ as a decimal number is $\boxed{\mathbf{0.00236}}$ .

11. How many significant figures are in 10.659 22?
Apply the rules for significant figures.
- All non-zero digits are significant (1, 6, 5, 9, 2, 2). There are 6 such digits.
- Zeros between non-zero digits are significant. The zero between 1 and 6 is significant. There is 1 such digit.
Count the total number of significant figures.
Total significant figures = 6 (non-zero digits) + 1 (trapped zero) = 7.
Answer:
The number 10.659 22 has $\boxed{\mathbf{7}}$ significant figures.

Here are the solutions to the next set of problems: 8. Write 0.416 666 667 correct to 3 significant figures. 9. Express 12 000 in Standard form. 10. Write 2.36 x 10⁻³ as a decimal number.

Step-by-step solution

Identify the first three significant figures.

Look at the fourth significant figure to determine rounding.

Round the third significant figure.

Place the decimal point after the first non-zero digit to get a number between 1 and 10.

Count how many places the decimal point was moved.

Write the number in standard form $a \times 10^n$ .

Identify the exponent of 10.

Move the decimal point.

Apply the rules for significant figures.

Count the total number of significant figures.

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