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.
<em>Alternate solution</em>
14₅ = 5+4 = 9₁₀ . . . now we can find the difference in base 10:
30 -9 = 21
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<em>Additional comment</em>
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 <em>any</em> number base, and they extend to either side of the "decimal point."
