Convert the following numbers into base 5 and verify:

(1) 52

(2) 70

(3) 95

(4) 120

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Solution

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Verification: 202₍₅₎

5²

5¹

5⁰

2

0

2

∴ 202₍₅₎ = 2 × 5² + 0 × 5¹ + 2 × 5⁰ = 52

Verification: 240₍₅₎

5²

5¹

5⁰

2

4

0

∴ 240₍₅₎ = 2 × 5² + 4 × 5¹ + 0 × 5⁰ = 70

Verification: 340₍₅₎

5²

5¹

5⁰

3

4

0

∴ 340₍₅₎ = 3×5² +4×5¹ + 0×5⁰ = 95

Verification: 440₍₅₎

5²

5¹

5⁰

4

4

0

∴ 440₍₅₎ = 4 × 5² + 4 × 5¹ + 0 × 5⁰ = 120

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Similar questions

Convert the following base 5 numbers into base 10.

(1) 20₍₅₎

(2) 44₍₅₎

(3) 304₍₅₎

(4) 403₍₅₎

(5) 1042₍₅₎

(6) 2010₍₅₎

(7) 2000₍₅₎

(8) 2341₍₅₎

(\frac{5}{4} + \frac{- 1}{2}) + \frac{- 3}{2} = \frac{5}{4} + (\frac{- 1}{2} + \frac{- 3}{2})

Convert the base 10 numbers into base 2 by division method.

(1) 2

(2) 6

(3) 18

(4) 22

(5) 30

(6) 44

(7) 51

(8) 63

(9) 77

(10) 100

1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7

∣ ∣ ∣ \frac{5}{4} + (\frac{- 3}{4}) ∣ ∣ ∣ < ∣ ∣ ∣ \frac{5}{4} ∣ ∣ ∣ + ∣ ∣ ∣ \frac{- 3}{4} ∣ ∣ ∣

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