# Correct rounding for sig-figs

## Homework Statement

A hotel elevator ascends 200m with maximum speed of 5m/s. Its acceleration and deceleration both have a magnitude of 1.0m/s^2
How far does the elevator move while accelerating to full speed from rest?

## The Attempt at a Solution

delta s = (5m/s)^2 / 1.0m/s^2
= 12.5m
but heres the thing confusing me about rounding.
The values given were written as 5m/s and 1.0m/s^2
When dividing (or multiplying) I thought we use the same number of sig-figs as the value with least amount of sig-figs, which would be "5"
But the answer is 12.5 --three sig-figs. I dont understand why.

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kuruman
Homework Helper
Gold Member
delta s = (5m/s)^2 / 1.0m/s^2
What equation are you invoking here? If it is 2aΔs = vf2 - vi2, what is Δs when vi = 0?
Aside from that, I think that whoever wrote this question was careless with significant figures. If the answer is given to 3 sig. figs, then all input quantities must also be given to 3 sig. figs.

delta s = (5m/s)^2 / 1.0m/s^2
= 12.5m
You are correct. By the rules of significant figures the answer should be 10.

A little off topic, but I thought I would point out that 5^2/1^2 does not equal 12.5. However, I’m sure that is just a typo. You lost something in the equation.

kuruman
Homework Helper
Gold Member
You are correct. By the rules of significant figures the answer should be 10.
I think you meant to write 1×101. It looks silly, but that's the rule for one sig. fig.

SammyS
Staff Emeritus
Homework Helper
Gold Member

## Homework Statement

A hotel elevator ascends 200m with maximum speed of 5m/s. Its acceleration and deceleration both have a magnitude of 1.0m/s^2
How far does the elevator move while accelerating to full speed from rest?

## The Attempt at a Solution

delta s = (5m/s)^2 / 1.0m/s^2
= 12.5m
but heres the thing confusing me about rounding.
The values given were written as 5m/s and 1.0m/s^2
When dividing (or multiplying) I thought we use the same number of sig-figs as the value with least amount of sig-figs, which would be "5"
But the answer is 12.5 --three sig-figs. I dont understand why.
Often an instructor or a textbook will give instructions to treat numbers given in problems as if they have 3 sig-figs, unless otherwise noted in problem instructions.

its a mastering physics question, so it wouldnt accept my answers until i inputed "12.5"
Im using the third equation of motion: (v_f)^2 = (v_i)^2 + 2a_s * delta s

Thanks for confirming. Im going to say something to prof cuz I lost points.

kuruman