Question

Average annual rainfall totals for cities in New York are listed below.

Rochester 0.97 meters
Ithaca 0.947 meters
Saratoga Springs 1.5 meters
New York City 1.268 meters

a. Put the rainfall measurements in order from least to greatest. Write the smallest total rainfall in word form and expanded form.
b. Round each of the rainfall totals to the nearest tenth.
c. Imagine New York City’s rainfall is the same every year. How much rain would fall in 100 years?
d. Write an equation using an exponent that would express the 100-year total rainfall. Explain how the digits have shifted position and why.

Answer 1

a) Order: 0.947 < 0.97 < 1.268 < 1.5

b)Smallest total rainfall = 0.947 meters in Ithaca

c) 100 years total rainfall =
`126.8 \text{ meters} = 1.268* 10^2`

Explanation:

We are given the following data in the question:

City: Rochester Ithaca Sara-Toga New-York

Rainfall(meters): 0.97 0.947 1.5 1.268

a) Order:

0.947 < 0.97 < 1.268 < 1.5

Ithaca < Rochester < New-York < Sara-Toga

Smallest total rainfall = 0.947 meters in Ithaca

Expanded form:
`0.947 = 9* (1)/(10) + 4*(1)/(100) + 7* (1)/(1000)`

Word form: seven thousandths and ninety four hundredths.

b) Round off to nearest tenths

Rochester - 1.0 meters

Ithaca - 0.9 meters

Sara-Toga - 1.5 meters

New-York - 1.3 meters

c)
`\text{Rainfall in 100 years} = \text{Annual rainfall}* 100 = 1.268* 100 = 126.8 \text{ meters}`

d) 100 years total rainfall =
`126.8\text{ meters} = 1.268* 10^2 = 0.1268* 10^3`

The points shifted because we have to multiply 1.268 by 100. This would again result in shifting the point towards right.