1 Express (a) 54,497 correct to the nearest tenth, (b) 0,000342 in standard form, (c) 478,367 correct to two…

Question

1 Express (a) 54,497 correct to the nearest tenth, (b) 0,000342 in standard form, (c) 478,367 correct to two significant figures.

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a) To express 54.497 correct to the nearest tenth, we look at the digit in the tenths place and the digit immediately to its right. Step 1: The digit in the tenths place is 4. The digit to its right is 9. Step 2: Since 9 ≥ 5, we round up the 4 to 5. All digits after the tenths place are dropped. 54.497 ≈ 54.5 The answer is 54.5 b) To express 0.000342 in standard form, we need to move the decimal point so that there is only one non-zero digit before it. Step 1: Move the decimal point to the right until it is after the first non-zero digit (3). 0.000342 → 3.42 Step 2: Count the number of places the decimal point was moved. It was moved 4 places to the right, so the exponent of 10 will be −4. 0.000342 = 3.42 × 10⁻⁴ The answer is 3.42 × 10⁻⁴ c) To express 478.367 correct to two significant figures, we identify the first two significant figures and then round. Step 1: The first significant figure is 4. The second significant figure is 7. The digit immediately to its right is 8. Step 2: Since 8 ≥ 5, we round up the second significant figure (7) to 8. The remaining digits to the left of the decimal point become zeros to maintain the place value. 478.367 ≈ 480 The answer is 480

1 Express (a) 54,497 correct to the nearest tenth, (b) 0,000342 in standard form, (c) 478,367 correct to two significant figures.

Answers

Step-by-step solution

Part a· 2 steps

The digit in the tenths place is 4.

Since $9 \ge 5$ , we round up the 4 to 5.

Part b· 2 steps
$3.42 \times 10^{-4}$

Move the decimal point to the right until it is after the first non-zero digit (3).

Count the number of places the decimal point was moved.

Part c· 2 steps480

The first significant figure is 4.

Since $8 \ge 5$ , we round up the second significant figure (7) to 8.

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1 Express (a) 54,497 correct to the nearest tenth, (b) 0,000342 in standard form, (c) 478,367 correct to two significant figures.

Answers

Step-by-step solution

Part a· 2 steps

The digit in the tenths place is 4.

Since 9≥59 \ge 59≥5, we round up the 4 to 5.

Part b· 2 steps3.42×10−43.42 \times 10^{-4}3.42×10−4

Move the decimal point to the right until it is after the first non-zero digit (3).

Count the number of places the decimal point was moved.

Part c· 2 steps480

The first significant figure is 4.

Since 8≥58 \ge 58≥5, we round up the second significant figure (7) to 8.

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Since $9 \ge 5$ , we round up the 4 to 5.

Part b· 2 steps
$3.42 \times 10^{-4}$

Since $8 \ge 5$ , we round up the second significant figure (7) to 8.