Category Archives: Metric Conversion

How to find circumference

How to find circumference

How to find circumference? A circle is an important shape in the mathematical world. There are a lot of problems involving it and it has many parts. It has a radius, diameter, circumference, center, arc, sector, segment etc. To find out each of them, there are different formula and techniques.  You will have to know the most common ones, that is the area of the circle.

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How to find circumference

How to find circumference

Let us see how we find the circumference. It is the outer part of the circle that gives it the round shape. You will have to know the diameter in order to find the circumference. The diameter is the line from one part of the circle to the other part and crossing through the center. The formula of circumference is circumference=2πr or πd. Based on the question, you decide which one to utilize.

Example: Find the circumference of a circle whose diameter is 5 inches.

Circumference = π x d (the question says diameter so we picked this one)

= 3.14 X 5 inches

= 15.7 inches (The unit will be the same as the unit of the diameter, for cm the result will be in cm)

The units are normally centimeters, meters or inches. If you order a pizza of 12 inches, that is the value of the diameter. The value of pi is 3.14159 but here we are using 3.14

To remember the formula or if you want to know how it originates, then read on:

π = Circumference / Diameter

We know that, diameter is radius plus radius

Therefore, it is 2r.

Now, multiply 2r with π and you will get the formula of the circumference.

People confuse the area of the circle with the circumference.

Look at the difference, one of them is about r² (area) while the other one is just the diameter which is 2r.

To remember them, you can start by memorizing them. Then, understand that the area is the square where is the circumference requires just the radius two time. You can rewrite the formula of circumference as

Circumference = 2 π r or π (r + r) AND Area = π r²

You can already see the difference and when you do the math, you will see that they are completely different.

Calculate the area and circumference of a circle with the radius 3 inches.

Area = π r²

= 3.14 x 3²

= 28.26 inches ² (The unit is inches’ square)

Circumference = 2 π r

C = 2 π r

= 2 x 3.14 x 3

= 18.84 inches

Now, you can tell that they are entirely different and avoid the confusion.

Tips

• If you are allowed to use calculators to solve this, consider purchasing one that has the built-in π so that you can solve the equations easily.

• Not every math problem will let you use pi according to your wish, you may have to use the fraction value which is

How to find horizontal asymptotes

How to find horizontal asymptotes

How to find horizontal asymptotes? The horizontal asymptote is a y-value present on graphs where a function goes by but never really touches it. The value for why will never be a zero. You can look closely when you see the graph, it will be a zero. They are going to meet the lines and intersect with some values of x and they maintain the same direction. You should know that it is a graph representing a function who will never come in contact.

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In this case, both of the polynomials are in second degree. It is the term that contains coefficients and variables that allows the usage of multiplication, addition and subtraction. If you are still not clear, look at the equations below.

How to find horizontal asymptotes

How to find horizontal asymptotes

x² + 5x + 9 has a single variable which is x.

x³ – 3xyz² + 5 has three variables which are x, y and z.

In the above example, when we said second degree it meant the power of them is square. For example, 4x², 5y² and 8z² are all second degree. If the polynomial is a zero it means that there are not terms at all. If you want to add a polynomial, it is quite simple

A = 3x² + 3x – 5

B = 6x² + 4x + 8

A + B = 9x² + 7x + 3

Here is how you can find the horizontal asymptote of the example given above,

Y =  which means y = 6.

When the polynomial is at different degrees, meaning the numerator has a value of x² and the denominator has a x without any power, then there is no horizontal asymptote.

Here is an example,

We can see that 12 has x and the x has a power of 2 or square. The denominator does have an x which does not have a power. Therefore, the result for this one is that there is no horizontal asymptote.

Here is another case,

Do not confuse them or get scared. Look closely at the degrees. The first step is to look at each of the values you have. It is the easiest one because you can see that the numerator has a less degree than the denominator. Here, the result is going to be y = 0. Whenever, you get a question where they have asked you solve the horizontal asymptotes of rational functions, look at the degrees. You will have three kinds of results. One is simplification.

Here is another example

Since, you know all the rules now, it should be easy to solve. You can see that both of them has square as the power. 15 and 5 are divisible. You can either write y =  or if the teacher asks you to write in the shortest term possible, simplify as much as you can. The result with be 3.

Tips

• The teacher may ask you draw a graph, for y = 3, draw a straight line using your scale on the y-axis where it is 3.

 

How to find standard deviation

How to find standard deviation?

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The formula for finding standard deviation is:

How to find standard deviation

Where s = sample standard deviation

wps872.tmp

∑ = sum of

Ӿ= sample mean

n = number of scores in sample

People think that finding out the standard deviation is nearly possible plus they face a lot of difficulties with it. It is quite simple and you need to follow the three steps. Are the products at the factory going out of order? How many people are taller than 5 feet 5 inches at the university? How long is it taking for the particle to decay? All of their answers can be found through standard deviation. Let us take an example, if there are five children and they all have different numbers of chocolate bars. One has 5 bars, the other has 6, the other has 7, following one has 8 and the last one has 10. If you are thinking of calculating the mean, you have to add all the numbers and divide by the number of children which is 5.

Calculation: 5 + 6 +7+8+10 = 36

36 ÷ 5 = 7.2

Here the Standard deviation is 1.92354 and the Variance (Standard deviation) is 3.7, the Population Standard deviation is 1.72047 and the Variance (Population Standard deviation) is 2.96. What you can see here that the mean and the standard deviation has a lot of difference. The standard deviation is a graph that looks like it is going up and down. If it was a straight line graph, then there would be no standard deviation. It is represented by sigma “σ” a Greek alphabet.

Let us see how we do it

Step 1: Find out the mean

Take the data you are provided with such as: 5, 10, 15, 20, 30

Mean = Sum of the 5 data ÷ Number of data

= (5+10+15+20+30) ÷ 5

= 80 / 5 = 16

Step 2: Find the variance

Subtract the mean from the given data,

5-16 = -11

10-16 = -6

15-16 = -1

20-16 = 4

30-16 = 14

Step 3: now find the square of the results you got

(-11) ² = 121

(-6) ² =36

(-1) ² = 1

(4) ² = 16

(14) ²= 196

Find the addition of the numbers you got after squaring: 121 + 36 + 1+ 16 +196 = 370. Divide the result with n-1 and n is the number of data you had at the start meaning 5.

370 / (5-1) = 270 / 4 = 92.5

Therefore, the variance is 92.5.

Step 3: To find the standard deviation, carry out the square root of the result you got as variance

√ (92.5)   therefore the result is 9.62.

For this one, variance (Standard deviation) = 92.5, Population Standard deviation=8.60233 and Variance (Population Standard deviation) =74.

Tips:

· While you are just learning it or doing it for the first time, make sure you have all the data and get everything you need like a calculator.

· Write down all the steps and do not skip any part thinking of short-cuts.

· Do your work neatly.

How to factor

How to factor? Are you scared of factor? Do you face trouble while doing these math’s?  They are not as hard as you think and since they are a part of algebra you will understand it once you start practicing. Let us start with knowing what is a factor. You are definitely familiar with the times table such as 3 X 3 = 9 or 4 X 3 = 12. The 3 and 4 are factors and the result is the product (9 and 12). It is a whole number that divides precisely into another number. Here are the whole numbers: 1, 2, 4, 8 and not 3 or 5.

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How big is an acre?

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Five or three are not whole numbers because you cannot divide them equally unlike the other numbers. Suppose, there are four sweets. You can divide them equally between two people. Two for each and you can divide the four sweets among four people and again equally. Therefore, you can say.

How to factor

2 x 2 = 4

4 x 1 =4

The factors are 2, 1 and 4.

Let us factor second degree polynomials. The format is ax2 + bx + c = 0

Rearrange your equation with the smallest one at the beginning such as 3 + 3x2 + 11x = 0

For example, you have an equation x²+ x + 12

x² + 4x – 3x +12

x(x+4) -3(x+4)

(x+4) (x-3) are factors.

Here is how you do it. First of all, look at the numbers. Arrange them and make sure there is no number on the other side, that means on the other side it should be zero. If the equation was x²+3x+12= -3x, rearrange them and make them as small as possible. It will be x²+ 3x+ 3x+ 12 =O, later add the two 3x and your final equation is x²+6x+12 as you have shortened it out, it is now ready to have its factors.

For the previous equation, if you had a zero at the end with an equal sign, you would have to find the value of the x. Then, the result would be x= -4 and x =3. Here is how you do it.

(x=4)(x-3)
x + 4 = 0 & x-3=0

x = -4          x= 3

Let us see how we got the 4 and 3. We look at the single number of the equation that does not have any x with it. In this case, it is the 12. Go through the times tables and think which numbers that can be multiplied to get 12 and also be added or subtracted to get 1. We know,

6 x 2 = 12

3 x 4 = 12

12 x 1 = 12

Adding or subtracting 6 and 2 will never get you 1 neither will 12 and 1. It is clear that 4 and 3 can be subtracted to get 1.

In case of simple equations, you will be able to figure it out yourself with just looking at it. For example, 4x²+ 4x+1 will result in (2x + 1) (2x +1) when you try to factor it.

How big is an acre?

How big is an acre? 43560 square feet is an acre.

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Let us examine the acre which is a popular term for calculating the size of lands. It could be that you heard someone is selling a specific number of acres of land and you are wondering what is the actual size. Is it big or is it small? It could be that your math papers require you to find out acres to all the units possible like square meters and square feet.

How big is an acre

You should keep in mind when dealing with acres that it can be in any shape like circles, square or rectangle. The rule is that it has to be 43 560 square feet no matter what its shapes. A regular shape of an acre is 660 feet by 66 feet. It is a usually misinterpreted information when looking for plots for a new home is that you should have minimum 1 acre of land in order to start construction.

 

Let us find by calculating:

660 feet X 66 feet = 42 560 square feet

Two feet make square feet.

If you are thinking of converting into other units, then you can first convert into another unit popular for measuring land which is the yard. It is 4840 square yard. There are two basic ways. One of them is through calculation and other is using formulae.

 

The first method

There are 0.00020661 acres in a square yard which means you have to multiply this with 4840 to get the result.

The result will be 0.9999924 which is approximately equal to 1.

0.00020661 X 4840 = 0.9999924 (approx. 1)

The second method

acres = feet square ÷ 4,840

The formula to convert from acres to ft. square is:

Feet square = acres x 4,840

 

If you are calculating in miles, then you should know that 1 acre is 0.0015625 square mile. 1 square mile is equal to 540 acres. To find out multiply by the factor or use the line “1 Square mile = 640 acre” Square mile is another popular unit used in both the British and American systems used to measure land. It goes like this, 1 square mile is 640 acres and 2 square miles is 1280 acre, 3 square miles is 1920 acre and so on.

To be more precise, 1 acre is 90 percent of a hundred yard or 91.44 meters long by 53.33 yards (48.76 meters) wide American field for football excluding the end zones. If you take into account the end zones, it will be about 1.32 acres.

1 Acre = 43,560 square feet

1 Acre = 160 square rods

1 Acre = 10 square chains

1 Acre = 160 square rods

1 Acre = 160 perches 1 Acre = 160 poles

1 Acre = .4047 hectare

1 Acre = 4047 square meters

1 Acre = is about 208 3/4 feet square

If you can remember them, you will be able to calculate the size of an acre using any formula.

How much does a gallon of milk weigh?

How much does a gallon of milk weigh? A gallon of milk weights about 8.6 pounds.

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The density of milk is about 1.03 kilograms per liter therefore 1 liter of milk weighs very near to 1 kilogram. There are many ways to calculate how much a gallon of milk weighs.  Everybody in every countries drink milk almost on a daily basis.

How much does a gallon of milk weigh

Children specially drink them every day. The first food of a newborn is the milk. Milk is an important source of food because it is one of the super drinks. It is just as good as an egg. It is full of nutrition. A glass of milk can provide you with enough energy to do a lot of work without getting tired or hungry. The farmers sell the milk and they are calculated in gallons. They send big trucks of milk from the farm to the city. The weight of the milk varies on the type of milk whether it is light or heavy. The heavy milk has a higher weigh per gallon than a light one.

Let us see how we can find how much a gallon of milk weighs. 

The answer is always in a decimal because we can never be sure about the precise weight as it is an organic product. Due to the fat present in milk, the weight can be different at different times. We know that 1 liquid gallon is equal to 128 fluid ounces. It means that 1 gallon is equal to more than 15 cups and 128 fluid ounces is equal to 4 liquid quarts.  You can first calculate how much is in 1 pound. Later, divide 1 by 16. Then, multiply with 128 fluid ounces.

Calculation:

1 gallon = 128 fluid ounce

1 pound = 16 fluid ounce

16 oz. = 1 lb.

1 oz. = (1 / 16) lb.

128 oz. = (1/16) X 128 = 8

It means that there is more than 8 pounds in a gallon of milk. It is slightly more than 8 because of its density and the fat content.

Another way to know is by knowing the amount of milk in liters. There is 3.79 liters in a gallon of milk. 3.79 liters is equal to 128.6 fluid ounces. 3.79 liters is 3.79 kilograms in case of water. We can use these term here because milk is 90 percent water. Hence 3.79 kilogram is 8.35552 pound. Again, we are with the result that a gallon of milk is more than 8 pounds.

Calculation: 

3.70 l = 3.79 kg

3.79 kg = 8.35552 pounds

How much is a ton

How much is a ton? A ton is 2000 pounds.

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A ton is unit used in both the British and American mathematical measurement system used to measure a number of things. First of all, let us talk about it when it is carrying goods from one country to another. When a ship carries 2000 pounds of good from one country to another we say that the ship is carrying a ton of goods. A metric ton is unit of weight equal to 1,000 kilograms which is 2,205 pounds. 1 Short ton in the US system is 907.18474 Kilograms and 1 Long Ton of the UK system is equal to 1 016.04691 Kilograms and one Metric Ton is equal to 1 000 Kilograms in both the US and UK systems.

How much is a ton

The ton is the American system is of 2000 pounds and the one in the UK and some of the other English speaking countries are 2240 pounds or 1016 kilograms. The ton is written as “T”. Kilogram is a base unit of mass in the metric system and equals to the mass of one liter of water.

 

Converting ton to kg: 

The abbreviation for kilogram is “kg”.1 kg is equal to 2.20462262 pounds. Since you know that a ton is 2000 pounds. You can find that 2000 pounds are 907.1847 kg. You can say that 1 ton is 907.1847 kg and 2000 pound. In the UK system, the ton is 1016.05 kg.

 

Calculation (US)

1 kg = 2.20462262 pounds

2.20462262 pounds = 1 kg

1 pound = 1 / 2.20462262 kg

1 pound = 0.4535923703803783kg

2000 pound = 0.4535923703803783 X 2000

Therefore the answer is 907.1847407607566 or 907.184 kg.

 

Calculation (British)

1 kg = = 2.20462262 pounds

2.20462262 pounds = 1 kg

1 pound = 1 / 2.20462262 kg

1 pound = 0.4535923703803783 kg

2240 pounds = = 0.4535923703803783kg X 2240

Therefore, the answer is 1016.046909652047 or 1016.045 kg

 

A ton is also used to measure money especially in the United States. You may have heard it a lot of times that someone lost a lot of money or someone requires a ton of money. There is actually a specific explanation. The original value never changed when it is about money. The ton is equal to 2000 pounds. In the American dollar note, they weigh one gram (1g). Around 454 grams make a pound, which results that a ton of dollar bills would be worth $908,000.

 

Calculation

1 ton = 2000 pounds

1 dollar = 1 gram (1 pound = 454 grams)

454 grams = 454 grams X 2000 pounds

Therefore, the result is $ 908000.

A ton of quarters make $40,000

A ton of pennies make $ 3632

 

1 Ton of Sand will take the space of 80 to 100 square feet at a 2 inch depth roughly. 1 Cubic Yard of Gravel can balance between 2,400 to 2,900 pounds or up to one and a half tons nearly. 1 Ton of Gravel will cover between 80 to 120 square feet at a 2 inch penetration approximately. Coal is also measured in tons.

How much does a gallon of water weigh?

How much does a gallon of water weigh? A gallon of water weighs 8.34 pounds.

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Gallon is commonly used to measure the capacity of a liquid like water, oil and ink. The British value for gallon was made for 10 pounds of water which is now popular as 4.54609 L or 10.02 pounds. The US liquid gallon is 231 cubic inches or 3.785 L. This means there is 8.3444 pounds of water. The dry US gallon is 268.8025 cubic inches and 4.405 l. This means 9.711 pounds of water.

How much does a gallon of water weigh?

You have to remember this method to know how much does a gallon of water weight. One gallon is 3.75 liters of water. 1 liter is equal to 1 kilogram. 1 gallon is approximately 3.75 kilograms. Therefore, 1 kilogram is equal to 2.2 pounds. 3.75 kilograms multiplied by 2.2 pounds will give the result of how much water there is in a gallon.

 

Calculation: 

1 gallon = 3.785 l

1 l =1 kg

1 gallon = 3.785 kg

1 kg =2.2 pounds

3.75 kg = 2.2 X 3.785 pounds

1 gallon = 8.33 pounds

 

How much does 5 gallons of water weigh? 

How much does 5 gallons of water weigh

5 gallons of water weigh 41.7 pounds

 

5 US fluid gallons is equal to 18.9270589 L. 1 gallon of water is equal to 3.78541178 liters and 5 gallons of water is equal to 8.9270589 liters. Since a liter of water has an index mass of 1, we can say that 1 l of water is 1 kg. 18.9270589 liters of water is equal to 18.9270589 kg because 3 kg of water is 3 liters, 50 kg of water is 50 liters. 5 gallons of water is equal to 18.9270589 kg. Let us convert it to pounds. We multiply 18.9270589 with 2.20462 which are 41.726972592118 pounds.

 

Calculation: 

5 gallons = 18.9270589 Liters

1 gallon = (18.9270589 Liters / 5 gallons)

1 gallon = 3.78541178 liters

5 gallons = 5 X 3.78541178 liters

5 gallons = 18.9270589 liters

Index mass of 1 l of water = 1

1 l = 1kg

18.9270589 kg = 18.9270589 liters of water

5 gallons = 18.9270589 kg

Converting in pounds, 18.9270589 x 2.20462 = 41.726972592118 pounds

The calculation is different in case of salt water because they have more weight.

 

How much does 10 gallons of water weigh?

How much does 10 gallons of water weigh?

10 gallons of water weigh 80 pounds

 

There are 8 pounds of water in a gallon. One pound is one-eighth of a gallon or 0.125 gallons. We need to convert it to 100 pounds. It should be less than 100 gallons. It takes more pounds to get 1 gallon. We either multiply or divide by 8 because multiplying or dividing by 1 gets us nothing. We will divide by 8 in this case.

 

Calculation: 

100 / 8 = 12.5 gallons

1000 X 0.125 = 12.5 gallons

For 10 gallons, 10 gallons X 8 = 80 pounds

Water with a specific gravity weighs 8.34 pounds as stated in the beginning.

You should know that pints and pounds are equal so you can say that there are 80 pints of water in 10 gallons.

How many milligrams (mg) in a gram (kilogram or ounce)

How many milligrams in a gram?  1000 milligrams in a gram. Gram is a unit in the mathematical measurement system used to measure weight for something small. If you are weighing something bigger use the kilogram. If you are measuring something smaller use a milligram.

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How many ounces in a cup (gallon, liter, pound, quart, pint, tablespoon, shot glass, gram)

How many oz. in a cup (gallon, pound, liter, quart, pint, lb., shot glass, ml, gram)

How many milliliters in a liter (gallon, quart, ounce, gram, centimeter, cup or pint)

Milligrams are used in cooking and in many other places of daily life. You can say that you need to add 3 milligrams of sugar to the tea. Grams are not used for only solids but they are also used for liquids. For example, one milliliter of water weighs one gram. The milligram is written as “mg”. The gram is written as “g”. The kilogram is written as “kg”.

How many milligrams in a gram

You need to remember these:

1. Milligrams (mg)

2. Centigrams (cg)

3. Grams (g)

4. Kilograms (kg)

From Number 1 to Number4, the value increases. 1 cg is bigger than 1 mg, 1 g is bigger than 1g and 1 kg is greater than 1g. You need to add a zero in your calculation as you go down. For example, 1 kg is equal to 100000 cg and 1000000 mg and 1000g.

There are many ways to find how many milligrams are in a gram. One way is to use a formula that is g =mg /1000 In place of g put 1 since you are looking for how much milligram is in a gram. Multiply 1 with 1000 to get the result.

Calculation: 

g =mg /1000

1 = mg/1000

Therefore, 1 X 1000 = 1000 milligrams

1000 mg equals how many grams

1000 mg equals 1 gram

3000 mg is equal to 3 grams, 2000 mg is equal to 2 grams and 1000 mg is equal to 1 gram. In this way you can find how much milligram is equal to a particular gram. Such as 51000 milligram is equal to 51 gram and 79 gram is equal to 79000 milligram.

 

How many milligrams in a kilogram 

How many milligrams in a kilogram

There are 1000000 milligrams in a kilogram.

Kilogram is a much bigger unit that gram. There are many ways to find out how many milligrams are in a kilogram. One of the basic way is to use the formula, kg =mg / 1000000. Here replace the kg with 1 since you are looking for 1 kg and multiply. People measure their weights in kilograms.

Calculation: kg =mg / 1000000

1 = mg/ 1000000

Therefore, the result is 1000000 milligrams. It has so many zeros because the kilometer stands on Number 4 on the list. The more you go down you add more zeros. An easy way to remember:

1 kilometer (km) = 100000 centigram (cg) = 1000 grams (g) = 1000000 milligram (mg)

 

How many milligrams in an ounce

How many milligrams in an ounce

29.5735 milligrams in an ounce

We know than 8 ounces make a cup and a cup contains 236.588 ml. If 8 ounces has 236.588 ml then 1 ounce should have 29.5735 milligrams.

Calculation: 8 ounces = 1 cup

8 ounces has 236.588 ml

1 ounce has (236.588 / 8) ml

1 ounce has 29.5735 ml

How many MB (megabytes) in a GB

How many MB in a GB? 1000 MB in a GB.

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The byte is a component of digital figures that most frequently contains of eight bits. Traditionally, the number of bits used to encode a single character of text in a computer was known as byte and this is why it is the littlest mentionable figure of memory in many computer designs. Let us make it simple for you, it is just a term used to measure the computer information. For example you use kilogram to measure mass. In fact, it is the SI unit of mass. We say the bag weighs 3 kg. In a similar way, we say my there are 50 GB space left on the drive. I need a new hard disk that can hold 500 GB. The symbol for gigabyte is GB or Gbyte. The gigabyte is made from megabytes. The symbol for megabyte is MB but occasionally MByte is used. The word “mega” is a multiplier of 1000000 (10 to the power 6) in the International System of Units (SI. Consequently, one megabyte is one million bytes of figures. Megabyte also can be measured as 102400 bytes.

How many MB in a GB

The value of 1 megabyte = 1000^2 bytes OR 1 megabyte = 1024^2bytes

1 MB = 1000000 bytes = 1000^2 B = 10^6 B

1 MB = 1024000 bytes = 1000×1024 B is the classification used to designate the formatted capacity of the 1.44 MB

So far, we are seeing that 1 MB being converted to bytes. Let us convert it to GB.

1 byte = 1e-9 GB

Most computers and many calculator programs present very big and very minor results in scientific notation. Since superscripted exponents like 10^7 cannot always be easily signified on computers and calculators, an alternative format is often used: the letter “e” or “E” signifies “times ten raised to the power”, thus substituting the ” × 10^ n”. The letter “e” is not linked to the calculated constant e (a confusion that is impossible when applying capital “E”); and though it stands for exponent, the notation is usually denoted to as (scientific) E system or (scientific) e notation, rather than (scientific) exponential notation.

1E-9 means 1.0x 10^-9.

1 GB = 1000000000 bytes

100000000 bytes = 1000 MB

We can conclude 1000 MB is in 1 GB.

 

How many megabytes are in a gigabyte?

How many megabytes are in a gigabyte?

1000 megabytes in a gigabyte

So far, we were using the short forms. The full form on MB is megabytes and the full form of GB is gigabytes. Mega means (10 to the power 6). For calculations we use the short forms. In sentences, you can write the full forms. Here are few examples:

· The SD card of my phone has 33 megabytes left

· All the folders take up to 5 gigabytes

· I have several megabytes left on my laptop

1 Gigabyte = 1000000000 bytes

100000000 bytes = 1000 megabyte

Therefore, 1000 megabyte = 1 gigabyte

We can conclude than 1000 megabytes are in 1 gigabyte.