Question

1. A barleycorn is an English unit of length equal to 1/3 of an inch. What is the height of the Empire State Building (449 m) expressed in barleycorn? (2.54 cm = 1 in)

a. 3 × 105 barleycorn b. 6 × 103 barleycorn c. 5 × 104 barleycorn d. 4 × 104 barleycorn e. 6 × 10–1 barleycorn​

Answer 1

c. 5 × 10⁴ barleycorn

Step-by-step explanation:

It is given that:

1 barleycorn = 1/3 of an inch

Convert 1 barleycorn into meter (m) units

1 inch = 2.54 cm

since 100 cm = 1 m

1 inch = 0.0254 m

Therefore 1/3 of an inch =
`(1)/(3) *0.0254 = 0.00847 m`

therefore:

1 barleycorn = 8.47*10⁻³ m

The height of the empire state building of 449 m would be:

`=(1\ barleycorn*449 m)/(8.47*10^(-3) m) = 5.3*10^(4)\ barleycorn`

Answer 2

449 m = 44900 cm

if 2.54 cm = 1 in

then 44900 cm = X in

X = (44900×1)/2.54 = 17677 in

if 1 barleycorn = 1/3 in

then Y barleycorn = 17677 in

Y = (17677×1)/(1/3) = 17677×3 = 53031 ≅ 5×
`10^(4)` barleycorns