Math Problem Statement

solve the following proble

Use the table below to answer questions A-C. Give the base for the place value table above.

Solution

The table shown appears to be a representation of a number in a certain positional numeral system. Let's break down how to solve the problem based on the table.

The table has columns labeled with "Place Value" and "Number." Here are the values:

Place Value128___16___1
Number21002

A) Give the base for the place value table above.

  1. The place values (128, 16, 1) suggest that these values are powers of a certain base.

    • 128=27128 = 2^7
    • 16=2416 = 2^4
    • 1=201 = 2^0

Since the place values are powers of 2, this table is in base 4 or quaternary system, as each step is skipping two powers of 2, based on the values shown.

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Math Problem Analysis

Mathematical Concepts

Place Value
Number Systems
Base Systems

Formulas

Place value in base systems is represented as powers of the base.
128 = 2^7, 16 = 2^4, 1 = 2^0

Theorems

Positional numeral system based on powers of a base

Suitable Grade Level

Grades 8-10