Question

SOMEONE PLISS ANSWER THIS... I NEED TO HAND IT IN NOW​

Answer 1

Answer:

  a) 151

  b) 160₉

  c)i) 30

  c)ii) 21

Step-by-step explanation:

(a) The value of the digits 3 and 4 is the value of the number with the other digits set to zero.

  304₇ = 3×7² +0×7¹ +4×7⁰ = 3×49 +4 = 151₁₀

The total value of the digits 3 and 4 is 151.

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(b) We can make a short table for conversions.

  10₁₀ = 11₉

  100₁₀ = (11₉)² = 121₉

So,

  135₁₀ = 1×121₉ +3×11₉ +5 = 121₉ +33₉ +5 = 154₉ +5 = 160₉

The base-9 equivalent of 135 is 160₉.

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(ci) 110₅ = 1×5² +1×5¹ +0×5⁰ = 25 +5 = 30₁₀

Lisa is 30 in base 10.

(cii) 110₅ -14₅ = 41₅ = 4×5¹ +1×5⁰ = 20+1 = 21₁₀

Lisa's younger brother is 21 in base 10.

Alternate solution

14₅ = 5+4 = 9₁₀ . . . now we can find the difference in base 10:

30 -9 = 21

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Additional comment

It helps to understand place value and how the digit positions relate to the powers of the number base. I find "expanded form using exponents" to be helpful, as you can see in the answers above. The relationships between place value and powers of the base hold true for any number base, and they extend to either side of the "decimal point."