Question

mr. haferd
percents level quiz 1 preparation
here is what is on the level 1 percents quiz: moving between decimal and percent representations, working with
icer\ percentages (like, \percent mental math #1\ from hw).
moving between decimal and percent representations:
below are two rulers that show how decimals and percents are related:
note that 0 = 0% and 1 = 100%. those are the two critical values to line up. everything else is proportional.

1. fill in the unlabeled tick marks on both scales.
2. add marks for 25% and 75% and for their decimal equivalents.
3. add marks for the decimal and percentage equivalents of the fractions $\frac{1}{3}$ and $\frac{2}{3}$
4. what patterns do you notice between the two scales?
5. where does 1% lie on the bottom scale? what is its decimal equivalent?

Explanation:

Step1: Fill unlabeled tick marks

Top decimal scale: Each tick = 0.1, so ticks are 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.1
Bottom percent scale: Each tick = 10%, so ticks are 0%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, 100%, 110%

Step2: Add 25%/75% & decimals

25% = $0.25$, 75% = $0.75$. Mark $0.25$ on top scale, 25% on bottom; mark $0.75$ on top, 75% on bottom.

Step3: Add 1/3, 2/3 equivalents

$\frac{1}{3} \approx 0.333 = 33.3\%$, $\frac{2}{3} \approx 0.667 = 66.7\%$. Mark $0.333$ & $0.667$ on top; 33.3% & 66.7% on bottom.

Step4: Identify scale pattern

Decimal value × 100 = percentage value.

Step5: Locate 1% and decimal

1% is 1/10 of the first 10% tick. 1% = $0.01$.

Answer:

1. Top decimal scale ticks: 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.1

Bottom percent scale ticks: 0%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, 100%, 110%

1. Mark $0.25$ (top) / 25% (bottom) and $0.75$ (top) / 75% (bottom)
2. Mark $0.333$ (top) / 33.3% (bottom) and $0.667$ (top) / 66.7% (bottom)
3. A decimal value multiplied by 100 equals its equivalent percentage value, and vice versa (percentage divided by 100 equals its decimal equivalent).
4. 1% lies 1/10 of the way from 0% to 10% on the bottom scale; its decimal equivalent is $0.01$