Question

1. mark -3/4 and -2/5 on the number line (2 marks)

Explanation:

Count the intervals on the number line

Using the Rational Numbers on Number Line knowledge point

$$
LATEXBLOCK0
$$

Determine the value of each tick mark

Using the Rational Numbers on Number Line knowledge point

$$
LATEXBLOCK1
$$

Locate the target rational numbers

To find where to place each number, we convert them to decimals or fractions with a denominator of 10:

• For \(-\frac{2}{5}\):

$$ -\frac{2}{5} = -\frac{4}{10} = -0.4 $$

This corresponds exactly to the 4th tick mark to the left of 0.

• For \(-\frac{3}{4}\):

$$ -\frac{3}{4} = -0.75 $$

This lies exactly halfway between \(-0.7\) (the 7th tick mark to the left of 0) and \(-0.8\) (the 8th tick mark to the left of 0).

Answer:

To mark the numbers on the given number line:

1. Identify the scale: The interval between \(-1\) and \(0\) is divided into \(10\) equal parts, meaning each tick mark represents a step of \(0.1\) (or \(-\frac{1}{10}\)) as you move left from \(0\).

1. Locate \(-\frac{2}{5}\):

$$ -\frac{2}{5} = -\frac{4}{10} = -0.4 $$

Place a mark exactly on the 4th tick mark to the left of 0.

1. Locate \(-\frac{3}{4}\):

$$ -\frac{3}{4} = -0.75 $$

Place a mark halfway between the 7th tick mark (\(-0.7\)) and the 8th tick mark (\(-0.8\)) to the left of 0.