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## Significant Figures Examples with Answers

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1. Find the Number of a Significant Figure in Each of the Following

(a) 8.4

(b) 173.6 m

(c) 407 g

(d) 4.68 m

(e) 8.1165 kg

(f) 0.054 km

(g) 0.00343 l

(h) 93.040 mg

(i) 30.030300 g

(j) 40.00 km

(k) 3.600 ml

(l) 70.002

## Solution:

(a) There are 2 significant figures available in 8.4. They are 8, 4.

(b) There are 4 significant figures available in 173.6 m. They are 1, 7, 3, and 4.

(c) There are 3 significant figures available in 407 g. They are 4, 0, and 7.

(d) There are 3 significant figures available in 4.68 m. They are 4, 6, and 8.

(e) There are 5 significant figures available in 8.1165 kg. They are 8, 1, 1, 6, and 5.

(f) There are 2 significant figures available in 0.054 km. They are 5, and 4.

(g) There are 3 significant figures available in 0.00343 l. They are 3, 4, and 3.

(h) There are 5 significant figures available in 93.040 mg. They are 9, 3, 0, 4, and 0.

(i) There are 8 significant figures available in 30.030300 g. They are 3, 0, 0, 3, 0, 3, 0, and 0.

(j) There are 4 significant figures available in 40.00 km. They are 4, 0, 0, and 0.

(k) There are 4 significant figures available in 3.600 ml. They are 3, 6, 0, and 0.

(l) There are 5 significant figures available in 70.002. They are 7, 0, 0, 0, and 2.

2. Round off each of the following correct up to 3 significant figures

(a) 57.3628 g

(b) 6.31874 kg

(c) 44.422 km

(d) 60.001 cm

(e) 0.0023596 m

(f) 0.0024030 l

## Solution:

(a) Given that 57.3628 g. It has 6 significant figures. To round off the given number into 3 significant digits, we need to round it off to 1 place after the decimal.

The digit 6 is greater than 5. So, the digit 3 becomes 4, and the digits 6, 2, and 8 disappear.

Therefore, 57.3628 g = 57.4 g rounded off to 3 significant figures.

(b) Given that 6.31874 kg. It has 6 significant figures. To round off the given number into 3 significant digits, we need to round it off to 2 places after the decimal.

The digit 8 is greater than 5. So, the digit 1 becomes 2, and the digits 8, 7, and 4 disappear.

Therefore, 6.31874 kg = 6.32 kg rounded off to 3 significant figures.

(c) Given that 44.422 km. It has 5 significant figures. To round off the given number into 3 significant digits, we need to round it off to 1 place after the decimal.

The digit 2 is less than 5. So, the digit 4 remains 4, and the digits 2, and 2 disappear.

Therefore, 44.422 km = 44.4 km rounded off to 3 significant figures.

(d) Given that 60.001 cm. It has 5 significant figures. To round off the given number into 3 significant digits, we need to round it off to 1 place after the decimal.

The digit 0 is less than 5. So, the digit 0 remains 0, and the digits 0, and 1 disappear.

Therefore, 60.001 cm = 60.0 cm rounded off to 3 significant figures.

(e) Given that 0.0023596 m. It has 5 significant figures. To round off the given number to 3 significant digits, we need to round it off to 5 places after the decimal.

The digit 9 is greater than 5. So, the digit 5 becomes 6, and the digits 9, and 6 disappear.

Therefore, 0.0023596 m = 0.00236 m rounded off to 3 significant figures.

(f) Given that 0.0024030 l. It has 5 significant figures. To round off the given number to 3 significant digits, we need to round it off to 5 places after the decimal.

The digit 3 is less than 5. So, the digit 0 remains 0, and the digits 3, and 0 disappear.

Therefore, 0.0024030 l = 0.00240 l rounded off to 3 significant figures.

3. Round off

(a) 16.367 g correct to the three significant figures.

(b) 0.00949 mg correct to the two significant figures.

(c) 0.005618 g correct to the one significant figures.

(d) 28.303 mm correct to the four significant figures.

(e) 33.422 km correct to the four significant figures.

(f) 4.0832 kg correct to the two significant figures.

(g) 0.004628 mm correct to the one significant figures.

## Solution:

(a) Given that 16.367 g. It has 5 significant figures. To round off the given number into 3 significant digits, we need to round it off to 1 place after the decimal.

The digit 6 is greater than 5. So, digit 3 becomes 4, and the digits 6, and 7 disappear.

Therefore, 16.367 g = 16.4 g rounded off to 3 significant figures.

(b) Given that 0.00949 mg. It has 3 significant figures. To round off the given number into 2 significant digits, we need to round it off to 4 places after the decimal.

The digit 9 is greater than 5. So, the digit 4 becomes 5, and the digit 9 disappear.

Therefore, 0.00949 mg = 0.0095 mg rounded off to 2 significant figures.

(c) Given that 0.005618 g. It has 4 significant figures. To round off the given number into 1 significant digit, we need to round it off to 3 places after the decimal.

The digit 6 is greater than 5. So, the digit 5 becomes 6, and the digits 6, 1, and 8 disappear.

Therefore, 0.005618 g = 0.006 g rounded off to 3 significant figures.

(d) Given that 28.303 mm. It has 5 significant figures. To round off the given number into 4 significant digits, we need to round it off to 2 places after the decimal.

The digit 3 is less than 5. So, the digit 0 remains 0, and the digits 3 disappear.

Therefore, 28.303 mm = 28.30 mm rounded off to 4 significant figures.

(e) Given that 33.422 km. It has 5 significant figures. To round off the given number to 4 significant digits, we need to round it off to 2 places after the decimal.

The digit 2 is less than 5. So, digit 2 remains 2, and the digits 2 disappear.

Therefore, 33.422 km = 33.42 km rounded off to 4 significant figures.

(f) Given that 4.0832 kg. It has 5 significant figures. To round off the given number to 2 significant digits, we need to round it off to 1 place after the decimal.

The digit 8 is greater than 5. So, the digit 0 becomes 1, and the digits 8, 3, and 2 disappear.

Therefore, 4.0832 kg = 4.1 kg rounded off to 2 significant figures.

(g) Given that 0.004628 mm. It has 4 significant figures. To round off the given number to 1 significant digit, we need to round it off to 3 places after the decimal.

The digit 6 is greater than 5. So, the digit 4 becomes 5, and the digits 6, 2, and 8 disappear.

Therefore, 0.004628 mm = 0.005 mm rounded off to 1 significant figure.

4. Round off

(a) $ 3067.665 to the nearest cents.

(b) 0.00588 m to the nearest cm.

(c) 18.0333 kg to the nearest g.

(d) $ 49.63 to the nearest dollar.

## Solution:

(a) Given that $ 3067.665. It has 7 significant figures. To round off the $ 3067.665 to the nearest cents, we need to round it off to 3 places after the decimal.

The digit 5 is equal to 5. So, digit 6 becomes 7, and the digit 5 disappear.

Therefore, $ 3067.665 = $ 3067.67

(b) Given that 0.00588 m. It has 3 significant figures. To round off the 0.00588 m to the nearest cm, we need to round it off to 3 places after the decimal.

The digit 5 is equal to 5. So, the digit 5 becomes 6, and the digit 8, and 8 disappear.

Therefore, 0.00588 m = 0.01 m.

(c) Given that 18.0333 kg. It has 6 significant figures. To round off the 18.0333 kg to the nearest g, we need to round it off to 3 places after the decimal.

The digit 3 is less than 5. So, the digit 3 remains 3, and the digits 3 disappear.

Therefore, 18.0333 kg = 18.033 kg.

(d) Given that $ 49.63. It has 4 significant figures. To round off the $ 49.63 to the nearest dollar, we need to round it off to the nearest number.

The digit $ 49.63 is closer to $ 50.

Therefore, $ 49.63 = $ 50.