GRE Decimals Questions Practice Questions with Answers

A decimal represents a fractional part of a whole number using a base-ten system indicated by a decimal point. On the GRE Quantitative Reasoning section, approximately 15% of questions involving arithmetic or algebra will require you to manipulate decimals, convert them to fractions, or round them to specific place values. Understanding how to navigate these values is essential for accuracy in both the calculator-assisted and non-calculator portions of the exam.

Success on the GRE depends on your ability to quickly transition between different numerical representations. While you have access to an on-screen calculator, relying on it for every minor calculation can drain your time. Instead, building a strong foundation in GRE Prep involves mastering the underlying logic of place value and significant figures. This article provides a deep dive into the mechanics of decimals, followed by targeted practice questions to sharpen your skills.

Concept Explanation

Decimals are a way of expressing numbers that fall between integers by using a point to separate the whole number from the fractional part. Each position to the right of the decimal point represents a power of 10 in the denominator. For example, the first digit to the right is the tenths place ($10^{-1}$), the second is the hundredths place ($10^{-2}$), and the third is the thousandths place ($10^{-3}$).

Key operations involving GRE Decimals Questions include:

• Addition and Subtraction: You must align the decimal points vertically to ensure you are adding or subtracting like place values.
• Multiplication: Multiply the numbers as if they were integers, then place the decimal point so the total number of decimal places in the product equals the sum of the decimal places in the factors.
• Division: Move the decimal point in the divisor to make it a whole number, and move the decimal in the dividend the same number of places. This is equivalent to multiplying both by a power of 10.
• Scientific Notation: Large or small numbers are often expressed as $a \times 10^n$, where $1 \leq a < 10$.

According to Wikipedia, the decimal system is the most widely used system for representing both integer and non-integer numbers globally. In the context of the GRE, you will frequently encounter "terminating" decimals (like 0.25) and "repeating" decimals (like 0.333...). Converting these to fractions (e.g., $\frac{1}{4}$ and $\frac{1}{3}$) is a common strategy to simplify complex algebraic expressions.

Solved Examples

Example 1: Multiplication and Place Value
Calculate the value of $0.04 \times 0.2$.

1. Ignore the decimals and multiply the integers: $4 \times 2 = 8$.
2. Count the total decimal places in the original numbers. $0.04$ has two places and $0.2$ has one place, for a total of three.
3. Place the decimal point in the result so it has three decimal places: $0.008$.

Example 2: Division with Decimals
Find the quotient of $0.125 \div 0.5$.

1. To make the divisor ($0.5$) a whole number, move the decimal point one place to the right to get $5$.
2. Move the decimal point in the dividend ($0.125$) one place to the right to get $1.25$.
3. Perform the division: $1.25 \div 5 = 0.25$.

Example 3: Comparing Decimals and Fractions
Which is larger: $0.66$ or $\frac{2}{3}$?

1. Convert the fraction to a decimal. $\frac{2}{3}$ is approximately $0.6666...$
2. Compare the place values. In the thousandths place, $\frac{2}{3}$ has a $6$, while $0.66$ (which is $0.660$) has a $0$.
3. Therefore, $\frac{2}{3} > 0.66$.

Practice Questions

1. What is the value of $0.003 \times 0.02$?

2. A merchant sells fabric for $4.50 per yard. If a customer buys 3.2 yards, what is the total cost?

3. Solve for $x$ in the equation: $$0.5x + 1.2 = 3.7$$

4. Arrange the following decimals in ascending order: $0.404, 0.044, 0.44, 0.0404$.

5. Express the fraction $\frac{7}{8}$ as a decimal.

6. If $y = 0.25$, what is the value of $\frac{1}{y^2}$?

7. A car travels 15.5 miles per gallon. How many gallons are needed for a 248-mile trip?

8. Round the result of $10.345 \times 2.1$ to the nearest hundredth.

9. Which is greater: $0.1^2$ or $0.1^3$?

10. Convert $0.125$ to its simplest fraction form.

Answers & Explanations

1. 0.00006: Multiply $3 \times 2 = 6$. There are three decimal places in $0.003$ and two in $0.02$, totaling five. Move the decimal five places left from 6.
2. $14.40: Multiply $4.5 \times 3.2$. $45 \times 32 = 1440$. With two total decimal places, the result is $14.40$.
3. 5: Subtract $1.2$ from both sides to get $0.5x = 2.5$. Divide $2.5$ by $0.5$, which is the same as $25 \div 5$, resulting in $5$.
4. 0.0404, 0.044, 0.404, 0.44: Compare by filling with trailing zeros: $0.0404, 0.0440, 0.4040, 0.4400$.
5. 0.875: Divide $7$ by $8$. $7.000 \div 8 = 0.875$.
6. 16: $y^2 = 0.25 \times 0.25 = 0.0625$. Alternatively, $y = \frac{1}{4}$, so $y^2 = \frac{1}{16}$. The reciprocal $\frac{1}{y^2}$ is $16$.
7. 16 gallons: Divide $248$ by $15.5$. This is equivalent to $2480 \div 155$. $155 \times 10 = 1550$; $2480 - 1550 = 930$. $155 \times 6 = 930$. So, $10 + 6 = 16$.
8. 21.72: $10.345 \times 2.1 = 21.7245$. The thousandths digit is 4, so we round down to $21.72$.
9. $0.1^2$: $0.1^2 = 0.01$ and $0.1^3 = 0.001$. Since $0.01 > 0.001$, the square is greater.
10. $\frac{1}{8}$: $0.125 = \frac{125}{1000}$. Dividing both numerator and denominator by 125 yields $\frac{1}{8}$.

1. What is the sum of 0.7, 0.07, and 0.007?

• A0.777
• B0.84
• C0.7077
• D7.77

Frequently Asked Questions

How do I quickly convert a fraction to a decimal without a calculator?

To convert a fraction to a decimal, divide the numerator by the denominator using long division. Alternatively, if the denominator can be easily converted to a power of 10 (like 5, 20, or 25), multiply both the numerator and denominator by the necessary factor to create a decimal fraction.

What is the difference between a terminating and a repeating decimal?

A terminating decimal has a finite number of digits after the decimal point, such as 0.5. A repeating decimal has one or more digits that repeat infinitely, such as 0.333..., and is often written with a bar over the repeating sequence.

Does the GRE calculator handle all decimal operations?

Yes, the on-screen GRE calculator can perform basic arithmetic with decimals. However, for many AI-powered style quantitative comparison questions, logical estimation or fraction conversion is often faster than typing into the interface.

How should I round decimals on the GRE?

Always follow the specific rounding instructions provided in the question stem, such as "round to the nearest tenth." If no instructions are given, keep as much precision as possible until the final step of your calculation to avoid cumulative rounding errors.

Why do decimals become smaller when squared?

When you square a positive decimal between 0 and 1, you are essentially taking a fraction of a fraction. For example, $0.5 \times 0.5$ is half of a half, which results in 0.25, a smaller value than the original 0.5.