Answer:
a) 151
b) 160₉
c)i) 30
c)ii) 21
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."