Complete the table below. Mark the approximate locations in the following diagram.

Question

Homi · Accepted Answer

We can convert percentages to fractions by dividing by 100 and to decimals by dividing by 100, and then represent these values on a number line.

Step 1 — Convert Percentages to Fractions

To convert a percentage to a fraction, we write the percentage value over 100. Then, we simplify the fraction.

Let us convert $90\%$ to a fraction:

$90\% = \frac{90}{100}$

$= \frac{9}{10}$

Let us convert $250\%$ to a fraction:

$250\% = \frac{250}{100}$

$= \frac{25}{10}$

$= \frac{5}{2}$

Let us convert $28.9\%$ to a fraction:

$28.9\% = \frac{28.9}{100}$

To remove the decimal, we multiply the numerator and denominator by 10:

$= \frac{28.9 \times 10}{100 \times 10}$

$= \frac{289}{1000}$

We apply this method to all percentages to find their fractional forms.

Step 2 — Convert Percentages to Decimals

To convert a percentage to a decimal, we divide the percentage value by 100. This is equivalent to moving the decimal point two places to the left.

Let us convert $90\%$ to a decimal:

$90\% = \frac{90}{100}$

$= \mathbf{0.90}$

Let us convert $173\%$ to a decimal:

$173\% = \frac{173}{100}$

$= \mathbf{1.73}$

Let us convert $28.9\%$ to a decimal:

$28.9\% = \frac{28.9}{100}$

$= \mathbf{0.289}$

We apply this method to all percentages to find their decimal forms.

Step 3 — Complete the Table

Using the conversion methods from Step 1 and Step 2, we complete the table.

Step 4 — Mark Locations on the Diagram

The diagram is a number line representing percentages from $0\%$ to $400\%$ . We will mark the approximate location of each percentage on this bar.

The original diagram already shows $90\%$ marked just before $100\%$ .

$110\%$ is slightly past $100\%$ .
$200\%$ is at the mark labeled (2).
$250\%$ is halfway between $200\%$ and $300\%$ .
$15\%$ is a small distance from $0\%$ .
$173\%$ is between $100\%$ and $200\%$ , closer to $200\%$ .
$358\%$ is between $300\%$ and $400\%$ , closer to $350\%$ .
$28.9\%$ is between $0\%$ and $100\%$ , closer to $0\%$ .
$305\%$ is slightly past $300\%$ .

Answer

(i) The completed table is:

| Percent | 90% | 110% | 200% | 250% | 15% | 173% | 358% | 28.9% | 305% | | :------ | :-- | :--- | :--- | :--- | :-- | :--- | :--- | :---- | :--- | | Fraction | 9/10 | 11/10 | 2/1 | 5/2 | 3/20 | 173/100 | 179/50 | 289/1000 | 61/20 | | Decimal | 0.9 | 1.1 | 2.0 | 2.5 | 0.15 | 1.73 | 3.58 | 0.289 | 3.05 |

(ii) The approximate locations marked on the diagram are:

Diagram 1

Question 12

Answer

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