Answer:
[tex]\sf 72\%,\:\: \dfrac{5}{4}, \:\: 1\frac{3}{4}, \:\:3.48[/tex]
Option D: 0.4, 1 ³/₅, 190%
Step-by-step explanation:
Question 6
Given data set:
[tex]\sf \dfrac{5}{4},\: 1 \frac{3}{4},\: 72\% \: \textsf{ and }\: 3.48[/tex]
Part A
To be able to easily order the given data, rewrite the numbers so that they are all in the same format.
The easiest form to use is decimal.
We can rewrite the fractions and percent with 100 as their denominators, then divide the numerator by 100 by simply moving its decimal point back two places.
[tex]\sf \dfrac{5}{4}=\dfrac{5 \times 25}{4 \times 25}=\dfrac{125}{100}=1.25[/tex]
[tex]\sf 1 \frac{3}{4}=\dfrac{1 \times 4+3}{4}=\dfrac{7}{4}=\dfrac{7 \times 25}{4 \times 25}=\dfrac{175}{100}=1.75[/tex]
[tex]\sf 72\% = \dfrac{72}{100}=0.72[/tex]
Therefore, the data set (in decimal form) from least to greatest is:
0.72, 1.25, 1.75, 3.48
Therefore:
[tex]\sf 72\%,\:\: \dfrac{5}{4}, \:\: 1\frac{3}{4}, \:\:3.48[/tex]
Part B
I rewrote the numbers in equivalent decimal form. The fractions and percent were easily converted to equivalent decimals by rewriting them so their denominators were 100, then dividing the numerator by 100 by moving its decimal point back 2 places.
Question 7
Given data values:
190%, 1 ³/₅ and 0.4
From inspection of the given answer options, each number line has the value of 0.4 in the correct place.
Convert the other two numbers to decimals:
[tex]\sf 190\%=\dfrac{190}{100}=1.9[/tex]
[tex]\sf 1 \frac{3}{5}=\dfrac{1 \times 5+3}{5}=\dfrac{8}{5}=\dfrac{8 \times 20}{5 \times 20}=\dfrac{160}{100}=1.6[/tex]
Therefore, the order of the given numbers from smallest to largest is:
0.4, 1.6, 1.9 ⇒ 0.4, 1 ³/₅, 190%
So the correct number line for the given values is the last option (see attached).
