Problem

Use the organizer and number line. Order these four values from least to greatest: \(0.68\); \(\text{seventy}\text{-}\text{two}~\text{hundredths}\); \(0.7~+~0.03\); and the blue point labeled \(0.705\) on the number line. Then find the closest pair of neighboring values in your ordered list.

A support graphic with a two-column organizer table and a number line. The table lists four given forms: 0.68, seventy-two hundredths, 0.7 + 0.03, and point on number line, with blank spaces to rewrite each as a decimal. The number line runs from 0.68 to 0.74 and shows a blue point labeled 0.705 halfway between 0.70 and 0.71.

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What this problem is really about

This problem has two linked tasks: put unlike representations on a common scale, then compare their spacing. We’ll convert every value to a decimal, align the place values, and order them. Once they are ordered, subtracting neighboring values will reveal which pair has the smallest gap.

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0.68 < 0.72 < 0.705 < 0.73; 0.72, 0.705

0.68 < 0.705 < 0.72 < 0.73; 0.72, 0.73

0.68 < 0.705 < 0.72 < 0.73; 0.705, 0.72

0.68 < 0.705 < 0.73; 0.705, 0.73

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Use the organizer and number line. Order these four values from least to greatest: \(0.68\); \(\text{seventy}\text{-}\text{two}~\text{hundredths}\); \(0.7~+~0.03\); and the blue point labeled \(0.705\) on the number line. Then find the closest pair of neighboring values in your ordered list.

What this problem is really about

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