Question

11 a submarines depth levels are recorded in the table at the right. order the numbers from the lowest depth to the highest dept.
depth
-2.1
-25.2
-21\frac{1}{5}
-25\frac{1}{4}
12 a runner wants to run the 100 - meter dash in 13 seconds or less. the table shows the difference between his goal and his actual times. order the differences from greatest to least.
race
differences between goal and actual time (s)
1
-1.3
2
2\frac{1}{10}
3
-\frac{1}{8}
4
2.2
13 which of the following numbers is closest to 1 whole?
a) 80%
b) 0.9
c) \frac{7}{8}
d) \frac{1}{2}
14 which of the following numbers has the greatest value?
a) 0.004
b) \frac{2}{5}
c) 3
d) 250%

Explanation:

Question 11

Step1: Convert mixed numbers to decimals

First, convert \(-21\frac{1}{5}\) and \(-25\frac{1}{4}\) to decimals. \(-21\frac{1}{5} = -21.2\) and \(-25\frac{1}{4} = -25.25\).

Step2: Compare the decimals

Now we have the numbers: \(-2.1\), \(-25.2\), \(-21.2\), \(-25.25\). For negative numbers, the larger the absolute value, the smaller the number. So, comparing the absolute values: \(25.25 > 25.2 > 21.2 > 2.1\). Therefore, the order from lowest (most negative) to highest (least negative) is \(-25\frac{1}{4}\), \(-25.2\), \(-21\frac{1}{5}\), \(-2.1\).

Step1: Convert mixed numbers to decimals

Convert \(2\frac{3}{10}\) to a decimal, which is \(2.3\).

Step2: Compare the numbers

We have the numbers: \(-1.3\), \(2.3\), \(-\frac{1}{8}=-0.125\), \(2.2\). Positive numbers are greater than negative numbers. Among positive numbers, \(2.3 > 2.2\). Among negative numbers, \(-0.125 > -1.3\) (since \(-0.125\) is closer to 0). So the order from greatest to least is \(2\frac{3}{10}\), \(2.2\), \(-\frac{1}{8}\), \(-1.3\).

Step1: Convert all options to decimals

• Option A: \(80\% = 0.8\)
• Option B: \(0.9\)
• Option C: \(\frac{7}{8}=0.875\)
• Option D: \(\frac{1}{2}=0.5\)

Step2: Find the difference from 1

• For A: \(|1 - 0.8| = 0.2\)
• For B: \(|1 - 0.9| = 0.1\)
• For C: \(|1 - 0.875| = 0.125\)
• For D: \(|1 - 0.5| = 0.5\)

The smallest difference is \(0.1\) (from option B).

Answer:

\(-25\frac{1}{4}\), \(-25.2\), \(-21\frac{1}{5}\), \(-2.1\)

Question 12