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Decimal Division and Approximation Practice Problems
Published on June 29, 2026
Pre-Algebra
Solve division problems with decimals, including non-terminating decimals, and practice rounding and truncating to a specified decimal place.
Question
Answer
Based on the image provided, here are the step-by-step solutions for the math problems:
2.a. Calculate
To perform this division, we can use long division:
-
: does not go into , so we put a and a decimal point. -
with a remainder of ( ). - Bring down a
to make it . with a remainder of ( ). - Bring down a
to make it . with a remainder of ( ). - The remainder
will keep repeating.
Result:
b. Does this division end? Explain.
No, the division does not end.
Explanation: The division results in a repeating decimal because the remainder
Explanation: The division results in a repeating decimal because the remainder
Exercise:3 (2 pts)
Write the quotients in the form of a fraction and solve:
a.
- As a fraction:
(by multiplying both numerator and denominator by ) - Solve:
b.
- As a fraction:
(by multiplying both numerator and denominator by ) - Solve:
Exercise:4 (3 pts)
Complete the following table:
| Quotient to be calculated | Results displayed | Approximate value to the nearest
|
Approximate value to the nearest
|
Cutting to
|
|---|---|---|---|---|
|
|
|
|
|
|
|
|
|
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Explanations for the table:
- Results displayed: The repeating decimal.
- By default (Rounding): If the next digit is
or more, round up. Here, the digit is , so we round up the digit. - By excess (Rounding up): Always round up to the next increment. In this case, it matches the default rounding.
- Cutting to
(Truncating): Simply stop at the third decimal place without rounding.