# Significant Figures Calculator

The Significant Figure Calculator uses the geometric shapes of a triangle and rectangle as an example for using Math and Physics formula to produce results that can then be used to illustrate the application of significant figures in Physics. The formula used in the geometric calculations is for example, you can access a comprehensive list of geometric calculators here including two dimensional shape calculators and three dimensional shape calculators.

Note that the Significant Figure Calculator uses inputs a, b and c for computation of triangle related formula and inputs a and b for rectangle related formula. The formula and computations will calculate for both metrics as the aim of this calculator is to illustrate the application of significant figures in the computation of Physics formula, not for specific geometric shape calculations which are available at the links mentioned above.

 🖹 Normal View🗖 Full Page View Length of the 1st side of the figure (a) m Length of the 2nd side of the figure (b) m Length of the 3nd side of the figure (c) m Mass of the object (m) kg Perpendicular Force (F) N Displacement (Δx) m Time (t) s Initial Velocity (u) m/s Final Velocity (v) m/s Volume of Substance (V) m3
Perimeter of Triangle Formula and Calculation Perimeter of Triangle (x) Perimeter of Rectangle (P) m Area of Rectangle (A) m2 Volume of Cuboid (V) m3 Density of a Substance (ρ) kg/m3 Pressure (P) N/m2 Average velocity (< v >) m/s Acceleration (a) m/s2 P = a + b + cP = + + P = m (metre) P = 2 × ( a + b )P = 2 × ( + )P = m (metre) A = a × bA = × A = m2 (square metre) V = a × b × cV = × × V = m3 (cubic metre) ρ = m/Vρ = /ρ = kg/m3 (kilogram per cubic metre) P = F/AP = /P = N/m2 (Newton per square metre) < v > = Δx/t< v > = /< v > = m/s (metre per second) a = v - u/ta = - /a = m/s2 (metre per square second) Length of the 1st side of the figure (a) m [metre] Length of the 2nd side of the figure (b) m [metre] Length of the 3nd side of the figure (c) m [metre] Mass of the object (m) kg [kilogram] Perpendicular Force (F) N [newton] Displacement (Δx) m [metre] Time (t) s [second] Initial Velocity (u) m/s [metre per second] Final Velocity (v) m/s [metre per second] Volume of Substance (V) m3 [cubic metre]

Please note that the formula for each calculation along with detailed calculations is shown further below this page. As you enter the specific factors of each significant figures calcualtion, the Significant Figures Calculator will automatically calculate the results and update the formula elements with each element of the significant figures calculation. You can then email or print this significant figures calculation as required for later use.

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Note that the Significant Figure Calculator uses inputs a, b and c for computation of triangle related formula and inputs a and b for rectangle related formula. The formula and computations will calculate for both metrics as the aim of this calculator is to illustrate the application of significant figures in the computation of Physics formula, not for specific geometric shape calculations which are available at the links mentioned above. ## Using the Sig Fig Calculator

The Significant figures Calculator (also known as a Sig Fig Calculator) is provided in support of our Physics Tutorials which cover all categories of Physics, a list of the PHysics categories covered is available at the end of this page. The calculation of significant figures in Physics is particularly important, particularly when computing long math equations. This Sig-Fig Calculator will calculate:

1. The sum of two similar physical quantities expressed in the correct number of significant figures
2. The difference of two similar physical quantities expressed in the correct number of significant figures
3. The product of two or three physical quantities expressed in the correct number of significant figures
4. The quotient of two physical quantities expressed in the correct number of significant figures

These results will be used to find the following physical quantities:

1. Perimeter of a triangle expressed in the correct number of significant figures if the side lengths are given
2. Perimeter of a rectangle expressed in the correct number of significant figures if the side lengths are given
3. Area of a rectangle expressed in the correct number of significant figures if the side lengths are given
4. Volume of a cuboid expressed in the correct number of significant figures if the side lengths are given
5. Density of a substance expressed in the correct number of significant figures if mass and volume are given
6. Pressure exerted on a surface expressed in the correct number of significant figures if the perpendicular force and the surface area are given
7. Average velocity of a moving object expressed in the correct number of significant figures if displacement and time are given
8. Acceleration of a moving object expressed in the correct number of significant figures if initial and final velocity and the moving time are given

## Significant Figures in Physics

The following rules are applied when dealing with significant figures in Physics and within the Significant Figure Calculator

### 1) Addition and Significant Figures in Physics

a) First, all numbers must be written at the same unit - into the largest one

For example, if we have 4.2 dm + 1.7 cm we write 4.2 dm + 0.17 dm

b) Then, the sum is calculated as usual

4.2 dm + 0.17 dm = 4.37 dm

c) The result is rounded to the number with the smallest decimal places. In our example, it must be rounded up to the nearest tenth of dm. Thus,

4.37 dm ≈ 4.4 dm

Even if there are more than two numbers, we use the same procedure.

#### Quantities we can find through addition

Perimeter of a figure, the Resultant of two or more forces, displacements, velocities, etc.

### 2) Subtraction and Significant Figures in Physics

The procedure is the same as for the addition.

a) First, all numbers must be written at the same unit - into the largest one. Then we continue with calculating the value.

For example, if we have

28.2 cm - 5.46 cm

We notice the numbers are already written in the same unit. Therefore, we don't need to apply the first rule.

Now, we can calculate the result through a simple calculator,

28.2 cm - 5.46 cm = 22.74 cm

b) and then we round the result at one decimal place to fit the least accurate measurement (the number with the least decimal places). Thus, we obtain

22.74 cm ≈ 22.7 cm

Even if there are more than two numbers, we use the same procedure.

#### Quantities we can find through subtraction

Change in position (displacement), change in velocity, etc.

### 3) Multiplication and Significant Figures in Physics

a) First, all numbers must be written at the same unit - into the largest one.

For example, if we have 25.3 cm × 5.2 dm we write 2.53 dm × 5.2 dm

b) Then we calculate the multiplication regularly

In our example, we have

2.53 dm × 5.2 dm = 13.156 dm2

c) The result is rounded to show as many decimal places as there are in the factor with the least decimal places × 2

In our example, the factor with the least decimal places is 5.2 cm. It has only 1 decimal place. Therefore, the result must contain 1 × 2 = 2 decimal places. Therefore, we obtain

13.156 dm2 ≈ 13.16 dm2

If there are three factors in a multiplication (such as when calculating the volume of objects), the result must show as many decimal places as there are in the factor with the least decimal places × 3.

For example, if the dimensions of a cuboid are 5.3 cm × 11 dm × 25 mm, first they must be converted into the least accurate quantity, i.e. in decimetres and then we calculate the mathematical value of multiplication.

Therefore, we have

V = 0.53 dm × 11 dm × 0.25 dm = 1.4575 dm3

The factor with the least decimal places (11 dm) contains no decimal places. Therefore, the result must contain 0 × 3 = 0 decimal places.

Hence, the result written in the correct number of significant figures is

1.4575 dm3 ≈ 1 dm3

#### Quantities we can find through multiplication

Area of a figure (with two factors), volume of objects (with three factors), work, kinetic energy, etc.

### 4) Division and Significant Figures in Physics

The procedure is identical as for multiplication. The only difference is that in division we cannot use more than two numbers (dividend and divisor).

Example: Power is calculated by dividing work and time. If work is 32.645 J and time is 5.8 s a normal calculator shows

P = W/t = 32.645 J/5.8 s = 5.62844827 W

However, we must write the result in 1 × 2 = 2 decimal places as time contains only one decimal place and therefore, the result must be written in two decimal places. Hence, we get

5.62844827 W ≈ 5.63 W

#### Quantities we can find through division

Velocity, acceleration, power, pressure, density, etc. You may also find the Exponents Calculator useful.