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Write 0.416 666 667 correct to 3 significant figures.

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4 parts
8

0.417\text{0.417}

9

1.2×1041.2 \times 10^4

10

2360\text{2360}

11

7 significant figures\text{7 significant figures}

Step-by-step solution

10 steps

Part 8· 3 steps

Write 0.416 666 667 correct to 3 significant figures.

  1. Identify the first three significant figures.

    The first non-zero digit is 4, so the first three significant figures are 4, 1, 6.

  2. Look at the fourth significant figure to determine rounding.

    The fourth significant figure is 6. Since 6 is 5 or greater, round up the third significant figure.

  3. Round the number.

    Rounding 0.416 up at the third significant figure gives 0.417.

    0.417\boxed{\text{0.417}}

Part 9

1.2×1041.2 \times 10^4

Express 12 000 in Standard form.

  1. Move the decimal point to get a number between 1 and 10.

    The decimal point in 12 000 is after the last zero. Move it to the left until it is after the first non-zero digit (1).

    12000.→1.200012000. \to 1.2000

    The number is 1.2.

  2. Count the number of places the decimal point moved.

    The decimal point moved 4 places to the left. This means the exponent for 10 is 4.

  3. Write the number in standard form.

    1.2×1041.2 \times 10^4 1.2×104\boxed{1.2 \times 10^4}

Part 10

2360\text{2360}

Write 2.36×1032.36 \times 10^3 as a decimal number (ordinary form).

  1. Identify the exponent of 10.

    The exponent is 3. This means the decimal point needs to move 3 places to the right.

  2. Move the decimal point.

    Start with 2.36. Move the decimal point 3 places to the right, adding zeros as placeholders.

    2.36→23.6→236.→2360.2.36 \to 23.6 \to 236. \to 2360. 2360\boxed{\text{2360}}

Part 11

7 significant figures\text{7 significant figures}

How many significant figures are in 10.659 22?

  1. Apply the rules for significant figures.

    • All non-zero digits (1, 6, 5, 9, 2, 2) are significant.
    • Zeros between non-zero digits (the 0 between 1 and 6) are significant.

  2. Count the significant figures.

    The digits are 1, 0, 6, 5, 9, 2, 2. All of these are significant.
    There are 7 significant figures.

    7 significant figures\boxed{\text{7 significant figures}}
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