Question

Pls help!!! Give steps

Problem 3 (Unit Conversion Review):
An exact conversion is 1 inch = 2.54 cm. From this fact, deduce how many
a) Feet in a meter to 2 decimal places, and
b) Kilometers in a mile to 2 decimal places (recall that a mile is 5280 feet)

Answer 1

Explanation:

1 foot = 12 * 2.54 cm.

Feet in a metre = 100 / ( 12*2.54

= 3.28

1 mile = 5280 * 12 * 2.54 cm

= ( 5280 * 12 * 2.54) / (100*1000)

= 1.61 km.

Answer 2

Explanation:

a) There are 12 inches in a foot, so we can write:

1 ft = 12 in

Since 1 inch = 2.54 cm, we can substitute to get:

1 ft = 12 in = 12 × 2.54 cm = 30.48 cm

There are 100 cm in a meter, so we can divide to get:

1 m = 100 cm

Therefore, we can convert feet to meters by dividing by the conversion factor:

1 m = 100 cm ÷ 30.48 cm/ft ≈ 3.28 ft

So, there are approximately 3.28 feet in a meter to 2 decimal places.

b) We know that 1 mile is equal to 5280 feet, and we just found that 1 foot is equal to 30.48 cm. To convert miles to kilometers, we need to first convert miles to feet and then feet to meters and finally meters to kilometers.

1 mile = 5280 feet

1 foot = 30.48 cm = 0.3048 m

1 kilometer = 1000 m

Now, we can substitute the conversion factors to get:

1 mile = 5280 feet = 5280 × 0.3048 m = 1609.344 m

Finally, we can convert meters to kilometers by dividing by 1000:

1 mile = 1609.344 m ÷ 1000 m/km ≈ 1.61 km

Therefore, there are approximately 1.61 kilometers in a mile to 2 decimal places.