Octal to Decimal Conversion Quiz for Grade 8

1. Convert the octal number 10 to decimal.

8

10

16

2

To convert the octal number 10 to decimal, multiply each digit by 8 raised to the power of its position, starting from the right (0). Here, 1 is in the 1's place (8^1) and 0 is in the 8's place (8^0). Thus, 1×8^1 + 0×8^0 = 8 + 0 = 8.

Explanation

To convert the octal number 10 to decimal, multiply each digit by 8 raised to the power of its position, starting from the right (0). Here, 1 is in the 1's place (8^1) and 0 is in the 8's place (8^0). Thus, 1×8^1 + 0×8^0 = 8 + 0 = 8.

2. What is the decimal equivalent of the octal number 25?

17

21

25

33

To convert the octal number 25 to decimal, multiply each digit by 8 raised to the power of its position, starting from the right (0). Thus, \(2 \times 8^1 + 5 \times 8^0 = 16 + 5 = 21\). Therefore, the decimal equivalent of the octal number 25 is 21.

Explanation

To convert the octal number 25 to decimal, multiply each digit by 8 raised to the power of its position, starting from the right (0). Thus, \(2 \times 8^1 + 5 \times 8^0 = 16 + 5 = 21\). Therefore, the decimal equivalent of the octal number 25 is 21.

3. Convert 37 (octal) to decimal.

28

31

37

64

To convert the octal number 37 to decimal, multiply each digit by 8 raised to the power of its position (from right to left, starting at 0). Thus, 3 × 8^1 + 7 × 8^0 = 3 × 8 + 7 × 1 = 24 + 7 = 31 in decimal.

Explanation

To convert the octal number 37 to decimal, multiply each digit by 8 raised to the power of its position (from right to left, starting at 0). Thus, 3 × 8^1 + 7 × 8^0 = 3 × 8 + 7 × 1 = 24 + 7 = 31 in decimal.

4. The octal number 100 equals ____ in decimal.

To convert the octal number 100 to decimal, each digit is multiplied by 8 raised to the power of its position, starting from the right (0). Thus, 1 × 8^2 + 0 × 8^1 + 0 × 8^0 equals 64 + 0 + 0, resulting in a decimal value of 64.

Explanation

To convert the octal number 100 to decimal, each digit is multiplied by 8 raised to the power of its position, starting from the right (0). Thus, 1 × 8^2 + 0 × 8^1 + 0 × 8^0 equals 64 + 0 + 0, resulting in a decimal value of 64.

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5. What is 52 (octal) in decimal form?

42

52

40

48

To convert the octal number 52 to decimal, multiply each digit by its corresponding power of 8. Here, 5 is in the 8's place (5 × 8^1 = 40) and 2 is in the 1's place (2 × 8^0 = 2). Adding these values together gives 40 + 2 = 42 in decimal.

Explanation

To convert the octal number 52 to decimal, multiply each digit by its corresponding power of 8. Here, 5 is in the 8's place (5 × 8^1 = 40) and 2 is in the 1's place (2 × 8^0 = 2). Adding these values together gives 40 + 2 = 42 in decimal.

6. Convert the octal number 77 to decimal.

56

63

77

49

To convert the octal number 77 to decimal, multiply each digit by 8 raised to the power of its position, starting from the right (0). Thus, 7 × 8^1 + 7 × 8^0 = 7 × 8 + 7 × 1 = 56 + 7 = 63. Therefore, the decimal equivalent of octal 77 is 63.

Explanation

To convert the octal number 77 to decimal, multiply each digit by 8 raised to the power of its position, starting from the right (0). Thus, 7 × 8^1 + 7 × 8^0 = 7 × 8 + 7 × 1 = 56 + 7 = 63. Therefore, the decimal equivalent of octal 77 is 63.

7. In octal to decimal conversion, what is the place value of the rightmost digit?

8

1

10

0

In octal (base 8) number system, each digit represents a power of 8. The rightmost digit corresponds to 8^0, which equals 1. Therefore, the place value of the rightmost digit in octal to decimal conversion is always 1, regardless of the overall number.

Explanation

In octal (base 8) number system, each digit represents a power of 8. The rightmost digit corresponds to 8^0, which equals 1. Therefore, the place value of the rightmost digit in octal to decimal conversion is always 1, regardless of the overall number.

8. The octal number 63 equals ____ in decimal.

To convert the octal number 63 to decimal, multiply each digit by its corresponding power of 8. The leftmost digit (6) is multiplied by 8^1 (which is 8), and the rightmost digit (3) is multiplied by 8^0 (which is 1). Thus, 6 × 8 + 3 × 1 equals 48 + 3, resulting in 51.

Explanation

To convert the octal number 63 to decimal, multiply each digit by its corresponding power of 8. The leftmost digit (6) is multiplied by 8^1 (which is 8), and the rightmost digit (3) is multiplied by 8^0 (which is 1). Thus, 6 × 8 + 3 × 1 equals 48 + 3, resulting in 51.

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9. What is the decimal value of octal 144?

100

96

144

112

To convert octal 144 to decimal, multiply each digit by the power of 8 based on its position: \(1 \times 8^2 + 4 \times 8^1 + 4 \times 8^0\). This calculates as \(1 \times 64 + 4 \times 8 + 4 \times 1 = 64 + 32 + 4 = 100\). Thus, the decimal value is 100.

Explanation

To convert octal 144 to decimal, multiply each digit by the power of 8 based on its position: \(1 \times 8^2 + 4 \times 8^1 + 4 \times 8^0\). This calculates as \(1 \times 64 + 4 \times 8 + 4 \times 1 = 64 + 32 + 4 = 100\). Thus, the decimal value is 100.

10. Convert 7 (octal) to decimal.

7

15

8

14

To convert the octal number 7 to decimal, you multiply each digit by 8 raised to the power of its position, starting from 0 on the right. Here, 7 is in the 0th position: 7 × (8^0) = 7 × 1 = 7. Thus, the decimal equivalent is 7.

Explanation

To convert the octal number 7 to decimal, you multiply each digit by 8 raised to the power of its position, starting from 0 on the right. Here, 7 is in the 0th position: 7 × (8^0) = 7 × 1 = 7. Thus, the decimal equivalent is 7.

11. Which power of 8 represents the second digit from the right in an octal number?

8⁰

8¹

8²

8³

In an octal number system, each digit represents a power of 8, with the rightmost digit being 8⁰. The second digit from the right corresponds to 8¹, which is equal to 8. Thus, the second digit represents the value of 8 in the octal system.

Explanation

In an octal number system, each digit represents a power of 8, with the rightmost digit being 8⁰. The second digit from the right corresponds to 8¹, which is equal to 8. Thus, the second digit represents the value of 8 in the octal system.

12. The octal number 201 equals ____ in decimal.

To convert the octal number 201 to decimal, multiply each digit by 8 raised to the power of its position, starting from the right (0). Thus, 2 × 8² + 0 × 8¹ + 1 × 8⁰ equals 2 × 64 + 0 × 8 + 1 × 1, which simplifies to 128 + 0 + 1, resulting in 129.

Explanation

To convert the octal number 201 to decimal, multiply each digit by 8 raised to the power of its position, starting from the right (0). Thus, 2 × 8² + 0 × 8¹ + 1 × 8⁰ equals 2 × 64 + 0 × 8 + 1 × 1, which simplifies to 128 + 0 + 1, resulting in 129.

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