Decimals and Coordinate Patterns

1. a) Write both numbers to the thousandths place:

$4.620$ and $4.602$

Since 620 thousandths is greater than 602 thousandths, 4.62 > 4.602.

b) Write both numbers to the thousandths place:

$0.750$ and $0.705$

Since 750 thousandths is greater than 705 thousandths, 0.75 > 0.705.

c) $12.3$ is the same as $12.30$, so 12.3 = 12.30.

2. a) In 6.248, the thousandths digit is 8, so round the hundredths digit up:

$6.248 \to 6.25$

b) In 0.995, the thousandths digit is 5, so round the hundredths digit up. This causes a regroup:

$0.995 \to 1.00$

c) In 14.673, the thousandths digit is 3, so keep the hundredths digit:

$14.673 \to 14.67$

3. a) Align decimal points:

$3.45 + 2.80 = 6.25$

b) Align decimal points:

$9.20 - 4.67 = 4.53$

c) Multiply as whole numbers first:

$125 \times 6 = 750$

Since 1.25 has two decimal places, place the decimal two places from the right:

$1.25 \times 6 = 7.50$

The answers are 6.25, 4.53, and 7.50.

4. a) The ordered pairs are (0, 2), (1, 5), (2, 8), (3, 11).

b) Each time x increases by 1, y increases by 3. The rule is:

$y = 3x + 2$

c) Substitute x = 4:

$y = 3 \times 4 + 2$

$y = 12 + 2$

$y = 14$

The next point is (4, 14).

5. a) Path A is horizontal because both points have y = 3.

$8 - 2 = 6$

Path A is 6 units long.

b) Path B is vertical because both points have x = 8.

$7 - 3 = 4$

Path B is 4 units long.

c) Add the path lengths:

$6 + 4 = 10$

The total length is 10 units.