Hello, and welcome come this video on ordering reasonable numbers! This video will present you just how to perform rational number from least to greatest or best to least.

You are watching: How can you order rational numbers from least to greatest

## Rational Number Definition

First, let’s evaluation the definition of a **rational number**. A rational number is any type of number that deserve to be turned into a portion with an integer in both the numerator and the denominator. (frac14) and (frac97) are examples of reasonable numbers. It’s likewise important to keep in mind that 0.25 and also 25% are likewise rational numbers since they are identical to (frac14) and also therefore have the right to be turned into a fraction that divides 2 integers.

## Ordering reasonable Numbers

among the easiest ways to stimulate rational numbers is to rotate them all into decimals and then put them in order. If we desire to revolve a **percentage right into a decimal**, all we perform is turn the percent sign right into a decimal suggest and relocate it two locations to the left. So 13% i do not care 0.13, and 213% becomes 2.13. Transforming fractions into decimals is a little bit more an overwhelming but still doable. To revolve a fraction into a decimal, we an initial have to remember the the portion bar means divide. This means that (frac34) is really the very same as (3div 4). For this reason if we desire to turn (frac34) into a decimal, we just use long division to divide (3div 4).

4 can’t go into 3 at all, therefore we include a decimal point and put a 0. Since we included a decimal point here, we need to include it to the optimal as well. 4 goes right into 30 7 times. (7 imes 4=28), so we write 28 and also subtract, and we’re left v 2. We then add another 0 and bring the down. And then check out 4 goes into 20 5 times. (4 imes 5=20), and when us subtract we acquire 0.

. | (7) | (5) | |||

(4phantom.) | (phantom.3) | . | (0) | (0) | |

(–) | (phantom.2) | (8) | |||

∨ (phantom.) | |||||

(2) | (0) | ||||

(–) | (2) | (0) | |||

(0) |

So (frac34=0.75).

Remember, some decimals proceed for a really lengthy time or end up repeating, so in these cases it could be valuable to ring to 3 or 4 decimal places. The should give you enough information to recognize where to location that number in a list.

One other thing we should look in ~ is how to stimulate square root of numbers. You can turn them right into decimals and also order them that way, but that is typically pretty tough to carry out without a calculator. Another means is to acknowledge what 2 numbers the square root drops between. Stop look at an example so ns can present you what I’m talking about.

41 is no a perfect square, for this reason the method to estimate its square root is to find the two perfect squares top top either next of it. The perfect square right listed below 41 is 36, and the one right above it is 49. Now, we recognize that the (sqrt36=6) and also the (sqrt49=7). So the (sqrt41) has actually to autumn somewhere in between 6 and also 7.

Notice, this doesn’t offer you a specific answer the what the(sqrt41) is in decimal form, but it provides you a basic location of wherein it would loss in a sequence of numbers, i m sorry is typically all that you need to put the in order.

Now the we have reviewed just how to order numbers, let’s exercise by placing this succession of number in stimulate from the very least to greatest:

We space going to start by turning each that these right into a decimal.

Remember, to turn a percent into a decimal, simply change the percent sign to a decimal allude and move it two places to the left, for this reason (87\%=0.87).

We can number out what (frac29) is by splitting (2div 9). Remember, a fraction bar always means divide!

So (2div 9): 9 goes into 2 zero times. Therefore we include a decimal and also put a 0; placing a decimal up here also. 9 goes right into 20 two times. (9 imes 2=18), and also then us subtract and get 2. If we include a 0 and bring it under we gain 20. 9 goes right into 20 2 times; we obtain 18, subtract, and get 2.

. | (2) | (2) | |||

(9phantom.) | (phantom.2) | . | (0) | (0) | |

(–) | (phantom.1) | (8) | |||

∨ (phantom.) | |||||

(2) | (0) | ||||

(–) | (1) | (8) | |||

(2) |

Notice that once we division we get (0.ar2), so because that this practice we will certainly round to 0.222.

When we look in ~ a square root, mental we desire to look because that the two perfect squares that the number drops between. 78 falls between the perfect squares 64 and 81, which are the squares that 8 and also 9 respectively. Therefore the (sqrt78) drops somewhere between 8 and 9.

(8

We can find (frac454) through dividing, just like we did with (frac29).

(1) | (1) | . | (2) | (5) | ||||

(4phantom.) | (phantom.4) | (5) | . | (0) | (0) | |||

(–) | (phantom.4) | |||||||

∨ (phantom.) | ||||||||

(phantom.0) | (5) | |||||||

(–) | (4) | |||||||

∨ (phantom.) | ||||||||

(1) | (0) | |||||||

(–) | (8) | |||||||

∨ (phantom.) | ||||||||

(2) | (0) | |||||||

(–) | (2) | (0) | ||||||

(0) |

So (frac454=11.25).

And 6.743 is already in decimal format, so us don’t need to do anything through that number.

Now, every we have to do is placed them in bespeak from the very least to greatest. Prior to I execute this, allow me erase few of our scratch work-related so us have much more room. Once we perform this, we get:

Now, this aren’t our initial values, therefore to gain our last answer, we have to adjust our decimal values back into their originals.

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If you to be asked to placed these number in order from biggest to least, you would follow all the exact same steps other than at the very end order lock opposite to just how we did that in this example, so (frac454) would be first and (frac29) would be last.

And that’s all there is come it! i hope this video on ordering reasonable numbers was helpful. Thanks for watching and happy studying!

order the following rational numbers from best to least: (2^2,40\%,4.53,frac194,frac256)