\( \newcommand{\abs}[1]{\left| \, {#1} \, \right| } \) \( \newcommand{\cm}{\mathrm{cm} } \) \( \newcommand{\sec}{ \, \mathrm{sec} \, } \) \( \newcommand{\units}[1]{\,\text{#1}} \) \( \newcommand{\vhat}[1]{\,\hat{#1}} \) \( \newcommand{\vhati}{\,\hat{i}} \) \( \newcommand{\vhatj}{\,\hat{j}} \) \( \newcommand{\vhatk}{\,\hat{k}} \) \( \newcommand{\vect}[1]{\boldsymbol{\vec{#1}}} \) \( \newcommand{\norm}[1]{\|{#1}\|} \) \( \newcommand{\arccot}{ \, \mathrm{arccot} \, } \) \( \newcommand{\arcsec}{ \, \mathrm{arcsec} \, } \) \( \newcommand{\arccsc}{ \, \mathrm{arccsc} \, } \) \( \newcommand{\sech}{ \, \mathrm{sech} \, } \) \( \newcommand{\csch}{ \, \mathrm{csch} \, } \) \( \newcommand{\arcsinh}{ \, \mathrm{arcsinh} \, } \) \( \newcommand{\arccosh}{ \, \mathrm{arccosh} \, } \) \( \newcommand{\arctanh}{ \, \mathrm{arctanh} \, } \) \( \newcommand{\arccoth}{ \, \mathrm{arccoth} \, } \) \( \newcommand{\arcsech}{ \, \mathrm{arcsech} \, } \) \( \newcommand{\arccsch}{ \, \mathrm{arccsch} \, } \)

17Calculus Physics - Significant Figures

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Single Variable Calculus
Derivatives
Integrals
Multi-Variable Calculus
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Functions

Significant Figures

Resources

It's time for complete disclosure.   I struggled A LOT with significant figures.   I would guess my way through them when I was in school and I did okay.   However, I probably would have done a lot better and, certainly, been less confused if I had mastered them out of the starting gate.   So this page is to help you master them BEFORE you need them.

Significant figures are important.   Rather than just writing down the numbers that come out of your calculator, they help you understand how exact your answer is.

And I found out that, when explained by someone who knows what they are doing, significant figures are not that difficult.   And, FINALLY, I understood them.   So watch these videos.   They are EXCELLENT.   If you feel like you already understand significant figures, the first one will be sufficient.   However, if you are hesitant AT ALL about significant figures, then watch the long one (speed up the video to get through it faster) because this guy knows what he is talking about.

The Organic Chemistry Tutor - Significant Figures - A Fast Review! [15min-8secs]

And if you're wondering how anyone could talk for over an hour and a half about significant figures, it's because he works LOTS of examples.

The Organic Chemistry Tutor - Significant Figures Made Easy! [1hr-36min-1sec]

AAAH!   Doesn't it feel great that you now understand significant figures?   Try the practice problems to show off your newly learned knowledge.

You Can Have an Amazing Memory: Learn Life-Changing Techniques and Tips from the Memory Maestro

Practice

Unless otherwise instructed, simplify the expression giving your answer with the correct significant digits.   Don't forget to use the inequality sign \(\approx\) to indicate that your answer is approximate.

Round 34718 to 1, 2, 3 and 4 significant figures.

Problem Statement

Round 34718 to 1, 2, 3 and 4 significant figures.

Solution

The Organic Chemistry Tutor - 4400 video solution

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Round 5726.302 to 1, 2, 3, 4 and 5 significant figures.

Problem Statement

Round 5726.302 to 1, 2, 3, 4 and 5 significant figures.

Solution

The Organic Chemistry Tutor - 4401 video solution

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\( 4.231 + 3.51 \)

Problem Statement

\( 4.231 + 3.51 \)

Solution

The Organic Chemistry Tutor - 4389 video solution

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\( 2.36 + 5.4 \)

Problem Statement

\( 2.36 + 5.4 \)

Solution

The Organic Chemistry Tutor - 4390 video solution

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\( 7.2361 + 8.42 \)

Problem Statement

\( 7.2361 + 8.42 \)

Solution

The Organic Chemistry Tutor - 4391 video solution

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\( 420. + 3.51 \)

Problem Statement

\( 420. + 3.51 \)

Solution

The Organic Chemistry Tutor - 4392 video solution

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\( 500 + 1.365 \)

Problem Statement

\( 500 + 1.365 \)

Solution

The Organic Chemistry Tutor - 4393 video solution

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\( 45300 + 176.21 \)

Problem Statement

\( 45300 + 176.21 \)

Solution

The Organic Chemistry Tutor - 4394 video solution

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\( 3.542 - 2.1 \)

Problem Statement

\( 3.542 - 2.1 \)

Solution

The Organic Chemistry Tutor - 4395 video solution

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\( 6.357 - 2.47 \)

Problem Statement

\( 6.357 - 2.47 \)

Solution

The Organic Chemistry Tutor - 4396 video solution

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\( 300 - 47.465 \)

Problem Statement

\( 300 - 47.465 \)

Solution

The Organic Chemistry Tutor - 4397 video solution

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\( 8.4 \times 5 \)

Problem Statement

\( 8.4 \times 5 \)

Solution

The Organic Chemistry Tutor - 4398 video solution

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\( 279 \times 83 \)

Problem Statement

\( 279 \times 83 \)

Solution

The Organic Chemistry Tutor - 4399 video solution

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\( 3.46 \times 2.1 \)

Problem Statement

\( 3.46 \times 2.1 \)

Solution

The Organic Chemistry Tutor - 4402 video solution

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\( 9.365 \times 14.315 \)

Problem Statement

\( 9.365 \times 14.315 \)

Solution

The Organic Chemistry Tutor - 4403 video solution

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\( \dfrac{32.6}{2.8} \)

Problem Statement

\( \dfrac{32.6}{2.8} \)

Solution

The Organic Chemistry Tutor - 4404 video solution

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\( 464.6895 \div 12.145 \)

Problem Statement

\( 464.6895 \div 12.145 \)

Solution

The Organic Chemistry Tutor - 4405 video solution

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\( (2.1 \times 10^3)(4 \times 10^5) \)

Problem Statement

\( (2.1 \times 10^3)(4 \times 10^5) \)

Solution

The Organic Chemistry Tutor - 4412 video solution

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\( (1.235 \times 10^5)(2.3 \times 10^6) \)

Problem Statement

\( (1.235 \times 10^5)(2.3 \times 10^6) \)

Solution

The Organic Chemistry Tutor - 4413 video solution

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\( (7.86 \times 10^3)(5.4 \times 10^2) \)

Problem Statement

\( (7.86 \times 10^3)(5.4 \times 10^2) \)

Solution

The Organic Chemistry Tutor - 4414 video solution

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\( \dfrac{9.37 \times 10^6}{2.4 \times 10^2} \)

Problem Statement

\( \dfrac{9.37 \times 10^6}{2.4 \times 10^2} \)

Solution

The Organic Chemistry Tutor - 4415 video solution

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\( 3.6 \times 4.639 + 5.831 \)

Problem Statement

\( 3.6 \times 4.639 + 5.831 \)

Solution

The Organic Chemistry Tutor - 4406 video solution

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\( 8.9 \times 3.564 + 2.316 \)

Problem Statement

\( 8.9 \times 3.564 + 2.316 \)

Solution

The Organic Chemistry Tutor - 4407 video solution

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\( \dfrac{9.24 - 1.342}{2.3} \)

Problem Statement

\( \dfrac{9.24 - 1.342}{2.3} \)

Solution

The Organic Chemistry Tutor - 4408 video solution

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\( \dfrac{7.856 + 8.23 + 11.4}{8.9} \)

Problem Statement

\( \dfrac{7.856 + 8.23 + 11.4}{8.9} \)

Solution

The Organic Chemistry Tutor - 4409 video solution

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\( 3.61 \times 10^3 + 5.1 \times 10^3 \)

Problem Statement

\( 3.61 \times 10^3 + 5.1 \times 10^3 \)

Solution

The Organic Chemistry Tutor - 4410 video solution

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\( 5.4 \times 10^3 + 2.1 \times 10^4 \)

Problem Statement

\( 5.4 \times 10^3 + 2.1 \times 10^4 \)

Solution

The Organic Chemistry Tutor - 4411 video solution

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Practice Search

Practice Instructions

Unless otherwise instructed, simplify the expression giving your answer with the correct significant digits.   Don't forget to use the inequality sign \(\approx\) to indicate that your answer is approximate.

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