Coding Camp: Progress Beyond the Display

Classify exact values and turn repeating decimals into fractions.

Read the Number Records

The coding camp tracks completed tasks and tests number-handling tools. Parentheses mark digits that repeat forever: 0.(23) = 0.232323… . Treat every value as exact unless rounding is stated.

Select every irrational value in the number-handling test file.

A test value has 50 nonrepeating decimal digits after the decimal point. After those digits, the block 803 repeats forever. What must be true?

A. The value is rational because its decimal eventually repeats.B. The value is rational only if the first 50 digits are zeros.C. The value is irrational because the repetition starts late.D. The value is irrational because its decimal never ends.

A debugging tool stores a signed correction as −23/80. Write its exact terminating decimal.

Decimal:

The camp is designing a decimal-view tool for real numbers. Which statement should appear in its documentation?

A. Only rational real numbers can be written in decimal form.B. Every real number has a decimal form that eventually repeats.C. Every real number has a decimal form, including irrational numbers.D. Only irrational real numbers have decimal forms that never end.

Recover Exact Fractions

Convert the stored decimals without rounding. Write fractions in simplest form.

A project file stores a progress factor as 0.(315). Convert it to a fraction.

0.(315) =

For n = 0.(52), a student subtracts n from 100n and obtains 99n = 52. Complete the fraction.

n = 52/

A progress factor is x = 0.2(7). Only the digit 7 repeats. Which fraction equals x?

A. 27/99B. 27/100C. 7/9D. 5/18

A small progress increment is 0.01(6). The digits 0 and 1 after the decimal point do not repeat; only 6 repeats. Convert it to a fraction.

0.01(6) =

A debugging record contains the signed adjustment −1.(08). Write it as a signed improper fraction.

−1.(08) =

Use Exact Progress

For each project, the completion share equals completed tasks divided by total tasks. Use exact fractions, not rounded decimals.

10.

Imani's project has 44 tasks. Its exact completion share is 0.(63). How many tasks are complete?

tasks

11.

Mateo's project has 60 tasks. Its exact completion share is 0.41(6), with only 6 repeating. How many tasks remain unfinished?

tasks

12.

A project dashboard reports an exact completion share of 0.(32). Which project record matches that share?

Project Records
Project	Completed tasks	Total tasks
Search	32	100
Chat	64	198
Calendar	32	90
Notes	64	200

A. The Search record matches.B. The Chat record matches.C. The Calendar record matches.D. The Notes record matches.

13.

A project export stores the exact completion share 4/33. Select every replacement that preserves the exact value.

14.

A camper claims that the progress share 4/7 might have a nonterminating, nonrepeating decimal. During long division by 7, the only possible nonzero remainders are 1, 2, 3, 4, 5, and 6. Use this fact to explain why the camper's claim cannot be correct. You do not need to calculate all the decimal digits.