Quiz about Pre-Algebra - Ch. 7.4 Extension Repeating Decimals Page 316-317

Question 1

Problem #5

STRUCTURE: In Example 1, why can you subtract the original equation from the new equation after multiplying by 10? Explain why these two steps are performed.

Accepted Answer

Multiply by 10 so that when you subtract the original equation, the repeating part is removed.

Answer

Multiply by 10 so that when you add the original equation, the repeating part is removed.

Question 2

Problem #5

STRUCTURE: In Example 1, why can you subtract the original equation from the new equation after multiplying by 10? Explain why these two steps are performed.

Accepted Answer

Because the solution does not change when adding/subtracting two equivalent equations.

Answer

Because the solution does change when adding/subtracting two equivalent equations.

Question 3

Problem #6

REPEATED REASONING: Compare the repeating decimals and their equivalent fractions in Exercises 1-4. Describe the pattern.

Accepted Answer

In Exercises 1-4, the common pattern was the denominator of 9.

Answer

In Exercises 1-4, the common pattern was the numerator of 9.

Question 4

Problem #6

REPEATED REASONING: Compare the repeating decimals and their equivalent fractions in Exercises 1-4. Describe the pattern. Use the pattern to explain how to write a repeating decimal as a fraction when only the tenths digit repeats.

Accepted Answer

Write the digit that repeats in the numerator and use 9 in the denominator.

Answer

Write the digit that repeats in the denominator and use 9 in the numerator.

Question 5

Problem #11

REPEATED REASONING: Find a pattern in the fractional representations of repeating decimals in which only the tenths and hundredths digits repeat.

Pattern: ___

Accepted Answer

PATTERN: Digits that repeat are in the numerator and 99 is in the denominator.

Answer

PATTERN: Digits that repeat are in the denominator and 99 is in the numerator.

Question 6

Problem #11

REPEATED REASONING: Find a pattern in the fractional representations of repeating decimals in which only the tenths and hundredths digits repeat. Use the pattern to explain how to write $$9.\overline{04}$$ as a mixed number.

Accepted Answer

Use 9 as the integer part, 4 as the numerator, and 99 as the denominator of the fractional part.

Answer

Use 9 as the integer part, 99 as the numerator, and 4 as the denominator of the fractional part.

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