Ordering Rational Numbers

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SSAT Upper Level: Quantitative › Ordering Rational Numbers

Questions 1 - 4
1

At a store, rank these discounts from smallest to largest value: $\frac{1}{5}$, $0.18$, $15%$, $\frac{3}{16}$, $0.22$.

$15%,\ 0.18,\ \frac{3}{16},\ \frac{1}{5},\ 0.22$

$15%,\ 0.18,\ \frac{1}{5},\ \frac{3}{16},\ 0.22$

$15%,\ 0.18,\ \frac{3}{16},\ 0.22,\ \frac{1}{5}$

$0.18,\ 15%,\ \frac{3}{16},\ \frac{1}{5},\ 0.22$

$15%,\ \frac{1}{5},\ 0.18,\ \frac{3}{16},\ 0.22$

Explanation

This question tests SSAT Upper Level quantitative skills: comparing and ordering integers and rational numbers. Students need to understand how to accurately compare and order numbers presented in various formats such as fractions, decimals, and percentages. For this question, the discounts must be arranged from smallest to largest by converting all values to decimals: 15% = 0.15, 1/5 = 0.20, 0.18 = 0.18, 3/16 = 0.1875, and 0.22 = 0.22. The correct answer is choice B because it accurately represents the numbers in the correct order: 15% (0.15), 0.18, 3/16 (0.1875), 1/5 (0.20), 0.22. A common mistake is shown in choice A, where students might place 1/5 before 3/16, not realizing that 1/5 = 0.20 is greater than 3/16 = 0.1875. To assist students: Encourage practice with converting between formats and stress the importance of attention to detail with decimal placement. Provide exercises that involve ordering mixed formats to develop flexibility in working with percentages, fractions, and decimals.

2

A science experiment lists solution concentrations: $0.125$, $\frac{1}{10}$, $13%$, $0.12$, $\frac{3}{25}$. Which is greatest?

$\frac{3}{25}$

$13%$

$0.125$

$0.12$

$\frac{1}{10}$

Explanation

This question tests SSAT Upper Level quantitative skills: comparing and ordering integers and rational numbers. Students need to understand how to accurately compare and order numbers presented in various formats such as fractions, decimals, and percentages. For this question, students must identify the greatest concentration by converting all to decimals: 0.125 = 0.125, 1/10 = 0.10, 13% = 0.13, 0.12 = 0.12, and 3/25 = 0.12. The correct answer is choice C because 13% = 0.13 is the largest value among all the options. A common mistake might be choosing choice B (0.125), where students might think the number with more decimal places is larger, not recognizing that 0.13 > 0.125. To assist students: Emphasize place value understanding and that 0.13 = 0.130 when comparing decimals. Provide exercises focusing on decimal comparison with different numbers of decimal places.

3

In a science lab, which recorded value is the greatest: $0.62$, $\frac{5}{8}$, $61%$, $0.59$, or $\frac{3}{5}$?

$0.59$

$61%$

$\frac{3}{5}$

$0.62$

$\frac{5}{8}$

Explanation

This question tests SSAT Upper Level quantitative skills: comparing and ordering integers and rational numbers. Students need to understand how to accurately compare and order numbers presented in various formats such as fractions, decimals, and percentages. For this question, students must identify the greatest value by converting all to decimals: 0.62 = 0.62, 5/8 = 0.625, 61% = 0.61, 0.59 = 0.59, and 3/5 = 0.60. The correct answer is choice B because 5/8 = 0.625 is the largest value among all the options. A common mistake might be choosing choice A (0.62), where students fail to recognize that 5/8 = 0.625 is actually greater than 0.62. To assist students: Encourage careful conversion of fractions to decimals and remind them that 5/8 means 5 ÷ 8. Provide practice problems that require finding the maximum or minimum value among mixed formats.

4

Which of the following lists these interest rates in ascending order: $12%$, $0.09$, $\frac{1}{10}$, $8%$, $0.11$?

$8%,\ \frac{1}{10},\ 0.09,\ 0.11,\ 12%$

$8%,\ 0.09,\ 0.11,\ \frac{1}{10},\ 12%$

$12%,\ 0.11,\ \frac{1}{10},\ 0.09,\ 8%$

$0.09,\ 8%,\ \frac{1}{10},\ 0.11,\ 12%$

$8%,\ 0.09,\ \frac{1}{10},\ 0.11,\ 12%$

Explanation

This question tests SSAT Upper Level quantitative skills: comparing and ordering integers and rational numbers. Students need to understand how to accurately compare and order numbers presented in various formats such as fractions, decimals, and percentages. For this question, the interest rates must be arranged in ascending order by converting all to decimals: 12% = 0.12, 0.09 = 0.09, 1/10 = 0.10, 8% = 0.08, and 0.11 = 0.11. The correct answer is choice A because it accurately represents the numbers in ascending order: 8% (0.08), 0.09, 1/10 (0.10), 0.11, 12% (0.12). A common mistake is shown in choice B, where students might incorrectly place 0.09 before 8%, not recognizing that 8% = 0.08 is smaller than 0.09. To assist students: Encourage practice with converting percentages to decimals by dividing by 100, and fractions to decimals through division. Provide exercises that mix all three formats to build confidence in ordering rational numbers.