Jonali goes to the market to buy spices. She purchases of Cinnamon, of Cumin seeds, of Cardamom and of Pepper. Express each of the quantities in kilograms by writing them in terms of fractions as well as decimals.

Understand the Question . To convert a quantity from grams to kilograms: As a fraction: Divide the number of grams by and simplify to the lowest terms. As a decimal: Divide the number of grams by (shift the decimal point places to the left). Part (i) Express of Cinnamon in kilograms as a fraction and a decimal. Step 1 · Convert to kilograms As a fraction As a decimal Answer > (i) (fraction) and (decimal) Part (ii) Express of Cumin seeds in kilograms as a fraction and a decimal. Step 1 · Convert to kilograms As a fraction As a decimal Answer > (ii) (fraction) and (decimal) Part (iii) Express of Cardamom in kilograms as a fraction and a decimal. Step 1 · Convert to kilograms As a fraction As a decimal Answer > (iii) (fraction) and (decimal) Part (iv) Express of Pepper in kilograms as a fraction and a decimal. Step 1 · Convert to kilograms As a fraction As a decimal Answer > (iv) (fraction) and (decimal) Common Mistakes Incorrect Decimal Shift: Moving the decimal point by places instead of places when dividing by (e.g. writing instead of ). Unsimplified Fractions: Leaving fractions unreduced (e.g. ) rather than expressing them in simplest form (). Multiplying Instead of Dividing: Multiplying by instead of dividing when converting from smaller units (grams) to larger units (kilograms).

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Question 2

Jonali goes to the market to buy spices. She purchases $50\text{ g}$ of Cinnamon, $100\text{ g}$ of Cumin seeds, $25\text{ g}$ of Cardamom and $250\text{ g}$ of Pepper. Express each of the quantities in kilograms by writing them in terms of fractions as well as decimals.

Solution

Understand the Question

$1\text{ kilogram} = 1000\text{ grams} \implies 1\text{ g} = \dfrac{1}{1000}\text{ kg}$ .
To convert a quantity from grams to kilograms:
- As a fraction: Divide the number of grams by $1000$ and simplify to the lowest terms.
- As a decimal: Divide the number of grams by $1000$ (shift the decimal point $3$ places to the left).

(i) Express $50\text{ g}$ of Cinnamon in kilograms as a fraction and a decimal.

Step 1 · Convert $50\text{ g}$ to kilograms

As a fraction

\begin{aligned} 50\text{ g} &= 50 \times \dfrac{1}{1000}\text{ kg} \\[0.6em] &= \dfrac{50}{1000}\text{ kg} \\[0.6em] &= \dfrac{5}{100}\text{ kg} \\[0.6em] &= \dfrac{1}{20}\text{ kg} \end{aligned}

As a decimal

\begin{aligned} 50\text{ g} &= \dfrac{50}{1000}\text{ kg} \\[0.6em] &= 0.050\text{ kg} \\[0.6em] &= 0.05\text{ kg} \end{aligned}

Answer

(i) $\dfrac{1}{20}\text{ kg}$ (fraction) and $0.05\text{ kg}$ (decimal)

(ii) Express $100\text{ g}$ of Cumin seeds in kilograms as a fraction and a decimal.

Step 1 · Convert $100\text{ g}$ to kilograms

As a fraction

\begin{aligned} 100\text{ g} &= 100 \times \dfrac{1}{1000}\text{ kg} \\[0.6em] &= \dfrac{100}{1000}\text{ kg} \\[0.6em] &= \dfrac{1}{10}\text{ kg} \end{aligned}

As a decimal

\begin{aligned} 100\text{ g} &= \dfrac{100}{1000}\text{ kg} \\[0.6em] &= 0.100\text{ kg} \\[0.6em] &= 0.1\text{ kg} \end{aligned}

Answer

(ii) $\dfrac{1}{10}\text{ kg}$ (fraction) and $0.1\text{ kg}$ (decimal)

(iii) Express $25\text{ g}$ of Cardamom in kilograms as a fraction and a decimal.

Step 1 · Convert $25\text{ g}$ to kilograms

As a fraction

\begin{aligned} 25\text{ g} &= 25 \times \dfrac{1}{1000}\text{ kg} \\[0.6em] &= \dfrac{25}{1000}\text{ kg} \\[0.6em] &= \dfrac{1}{40}\text{ kg} \end{aligned}

As a decimal

\begin{aligned} 25\text{ g} &= \dfrac{25}{1000}\text{ kg} \\[0.6em] &= 0.025\text{ kg} \end{aligned}

Answer

(iii) $\dfrac{1}{40}\text{ kg}$ (fraction) and $0.025\text{ kg}$ (decimal)

(iv) Express $250\text{ g}$ of Pepper in kilograms as a fraction and a decimal.

Step 1 · Convert $250\text{ g}$ to kilograms

As a fraction

\begin{aligned} 250\text{ g} &= 250 \times \dfrac{1}{1000}\text{ kg} \\[0.6em] &= \dfrac{250}{1000}\text{ kg} \\[0.6em] &= \dfrac{1}{4}\text{ kg} \end{aligned}

As a decimal

\begin{aligned} 250\text{ g} &= \dfrac{250}{1000}\text{ kg} \\[0.6em] &= 0.250\text{ kg} \\[0.6em] &= 0.25\text{ kg} \end{aligned}

Answer

(iv) $\dfrac{1}{4}\text{ kg}$ (fraction) and $0.25\text{ kg}$ (decimal)

Common Mistakes

Incorrect Decimal Shift: Moving the decimal point by $2$ places instead of $3$ places when dividing by $1000$ (e.g. writing $25\text{ g} = 0.25\text{ kg}$ instead of $0.025\text{ kg}$ ).
Unsimplified Fractions: Leaving fractions unreduced (e.g. $\dfrac{50}{1000}\text{ kg}$ ) rather than expressing them in simplest form ( $\dfrac{1}{20}\text{ kg}$ ).
Multiplying Instead of Dividing: Multiplying by $1000$ instead of dividing when converting from smaller units (grams) to larger units (kilograms).

Question 2

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