The volume of water in a tank is 2998673 extm3. What is the place value of digit 2 in the number?

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14. The volume of water in a tank is $2998673 \text{m}^3$ . What is the place value of digit 2 in the number? (2 marks)

Identify the number and the digit in question.
The number is 2,998,673. The digit is 2.
Determine the place value of each digit from right to left.
3 is in the ones place.
7 is in the tens place.
6 is in the hundreds place.
8 is in the thousands place.
9 is in the ten thousands place.
9 is in the hundred thousands place.
2 is in the millions place.
The place value of digit 2 is $\boxed{\text{Millions}}$ .

15. Kimani's plot of land is in the shape below. Calculate its area in hectares. (3 marks)
Identify the shape and its dimensions.
The plot is a right-angled triangle with base $600 \text{ m}$ and height $800 \text{ m}$ . The hypotenuse is $1000 \text{ m}$ .
Calculate the area of the triangle in square meters.
The formula for the area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$ .
$\text{Area} = \frac{1}{2} \times 600 \text{ m} \times 800 \text{ m}$ $\text{Area} = 300 \text{ m} \times 800 \text{ m}$ $\text{Area} = 240000 \text{ m}^2$
Convert the area from square meters to hectares.
We know that $1 \text{ hectare} = 10000 \text{ m}^2$ .
$\text{Area in hectares} = \frac{240000 \text{ m}^2}{10000 \text{ m}^2/\text{hectare}}$ $\text{Area in hectares} = 24 \text{ hectares}$
The area of the plot is $\boxed{24 \text{ hectares}}$ .

16. Patrick spent $\frac{1}{4}$ of his salary on rent and $\frac{2}{3}$ on food. What was the total fraction spent? (3 marks)
Identify the fractions spent.
Fraction on rent = $\frac{1}{4}$
Fraction on food = $\frac{2}{3}$
Add the fractions to find the total fraction spent.
To add fractions, find a common denominator. The least common multiple of 4 and 3 is 12.
$\text{Total fraction spent} = \frac{1}{4} + \frac{2}{3}$
Convert the fractions to have the common denominator.
$\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$ $\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$
Add the fractions with the common denominator.
$\text{Total fraction spent} = \frac{3}{12} + \frac{8}{12}$ $\text{Total fraction spent} = \frac{3 + 8}{12}$ $\text{Total fraction spent} = \frac{11}{12}$
The total fraction spent was $\boxed{\frac{11}{12}}$ .

The volume of water in a tank is 2998673 extm3. What is the place value of digit 2 in the number?

Step-by-step solution

Identify the number and the digit in question.

Determine the place value of each digit from right to left.

Identify the shape and its dimensions.

Calculate the area of the triangle in square meters.

Convert the area from square meters to hectares.

Identify the fractions spent.

Add the fractions to find the total fraction spent.

Convert the fractions to have the common denominator.

Add the fractions with the common denominator.

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